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currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBSY7
%!PS-AdobeFont-1.1: CMBSY7 001.000
%%CreationDate: 1992 Oct 22 12:18:11
% Computer Modern fonts were designed by Donald E. Knuth.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (001.000) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMBSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /prime put
readonly def
/FontBBox{0 -927 1542 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMIB10
%!PS-AdobeFont-1.1: CMMIB10 1.100
%%CreationDate: 1996 Jul 23 07:54:00
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMIB10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMIB10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 80 /P put
readonly def
/FontBBox{-15 -250 1216 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 80 /summationtext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 78 /N put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
dup 92 /angle put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 15 /bullet put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 26 /propersubset put
dup 33 /arrowright put
dup 50 /element put
dup 54 /negationslash put
dup 59 /emptyset put
dup 82 /R put
dup 91 /union put
dup 102 /braceleft put
dup 103 /braceright put
dup 110 /backslash put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 34 /epsilon put
dup 61 /slash put
dup 79 /O put
dup 105 /i put
dup 106 /j put
dup 107 /k put
readonly def
/FontBBox{0 -250 1171 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 61 /equal put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 65 /A put
dup 73 /I put
dup 76 /L put
dup 80 /P put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 116 /t put
dup 118 /v put
dup 123 /endash put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTT8
%!PS-AdobeFont-1.1: CMTT8 1.0
%%CreationDate: 1991 Aug 20 16:46:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 64 /at put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 122 /z put
readonly def
/FontBBox{-5 -232 545 699}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 16 /dotlessi put
dup 19 /acute put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 88 /X put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 127 /dieresis put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /asteriskmath put
dup 107 /bardbl put
dup 120 /section put
dup 121 /dagger put
dup 122 /daggerdbl put
dup 123 /paragraph put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 50 /two put
dup 58 /colon put
dup 63 /question put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 73 /I put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 13 /gamma put
dup 25 /pi put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 71 /G put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 97 /a put
dup 98 /b put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 110 /n put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSSBX10
%!PS-AdobeFont-1.1: CMSSBX10 1.0
%%CreationDate: 1991 Aug 20 16:43:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSSBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSSBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 45 /hyphen put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 73 /I put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-71 -250 1099 780}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 3 /asteriskmath put
dup 48 /prime put
dup 107 /bardbl put
dup 120 /section put
dup 121 /dagger put
dup 122 /daggerdbl put
dup 123 /paragraph put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 19 /acute put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
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dup 83 /S put
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dup 85 /U put
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dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 124 /emdash put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSS10
%!PS-AdobeFont-1.1: CMSS10 1.0
%%CreationDate: 1991 Aug 20 17:33:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSS10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 55 /seven put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 71 /G put
dup 79 /O put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 121 /y put
dup 123 /endash put
readonly def
/FontBBox{-61 -250 999 759}readonly def
currentdict end
currentfile eexec
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@endspecial -225 1781 a(Figure)40 b(2:)62 b(Six)41 b(segmen)n(ts)f
(for)g(whic)n(h)g(an)n(y)g(v)-5 b(arian)n(t)40 b(of)g(the)-225
1881 y(sw)n(eepline)27 b(sc)n(heme)g(leads)g(to)h(a)f(dual)g(graph)g
(with)h(a)f(bridge.)-142 2079 y(In)32 b(this)f(note)h(w)n(e)f(sho)n(w)g
(ho)n(w)f(to)i(\014nd)g(a)f(con)n(v)n(ex)f(partition)-225
2179 y(whose)d(dual)g(graph)g(has)g(no)g(bridges:)-225
2359 y Fk(Theorem)k(1)42 b Fo(F)-6 b(or)25 b(any)h(\014nite)f(set)g(of)
h(disjoint)h(line)f(se)l(gments)-225 2459 y(in)e(the)h(plane,)i(one)d
(c)l(an)h(c)l(onstruct)e(a)i(c)l(onvex)f(p)l(artition)h(whose)-225
2559 y(dual)30 b(gr)l(aph)h(is)f(2-e)l(dge)h(c)l(onne)l(cte)l(d.)-142
2739 y Fs(W)-7 b(e)40 b(giv)n(e)f(an)h(algorithm)f(for)g(constructing)g
(suc)n(h)h(a)f(con-)-225 2839 y(v)n(ex)26 b(partition.)37
b(Its)27 b(run)n(time)g(is)g Fp(O)r Fs(\()p Fp(n)966
2808 y Fj(4)p Fi(=)p Fj(3+)p Fi(")1153 2839 y Fs(\))g(for)g
Fp(n)g Fs(input)h(seg-)-225 2938 y(men)n(ts,)44 b(dominated)c(b)n(y)g
(2)p Fp(n)g Fs(ra)n(y)e(sho)r(oting)i(queries)g(among)-225
3038 y Fp(O)r Fs(\()p Fp(n)p Fs(\))26 b(p)r(olygonal)d(ob)5
b(jects,)24 b(one)g(for)g(eac)n(h)g(segmen)n(t)g(endp)r(oin)n(t.)-142
3137 y(Theorem)30 b(1)g(do)r(es)g(not)g(solv)n(e)f(Problem)h(1.)45
b(Fig.)30 b(3)g(depicts)-225 3237 y(four)c(segmen)n(ts)f(and)h(a)f(con)
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3636 y(dual)k(graph)f(of)h(the)h(con)n(v)n(ex)e(partition)g(w)n(e)h
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@endspecial -225 4893 a(Figure)21 b(3:)34 b(A)22 b(con)n(v)n(ex)e
(partition)h(whose)g(dual)h(graph)e(is)i(2-edge)-225
4993 y(connected)27 b(but)i(cannot)e(b)r(e)h(split)g(in)n(to)f(t)n(w)n
(o)g(spanning)g(trees.)-142 5191 y(F)-7 b(or)30 b Fp(n)g
Fs(disjoin)n(t)g(segmen)n(ts)f(in)h(the)h(plane,)g(it)f(is)g(natural)g
(to)-225 5291 y(de\014ne)h(a)g(smaller)e(family)i(of)g(con)n(v)n(ex)f
(partitions,)h(where)f(the)-225 5390 y(t)n(w)n(o)24 b(endp)r(oin)n(ts)h
(of)g(eac)n(h)f(segmen)n(t)g(should)h(b)r(e)g(consecutiv)n(e)f(in)-225
5490 y(the)i(p)r(erm)n(utation)f Fp(\031)j Fs(\(practically)-7
b(,)25 b(extending)h(eac)n(h)e(segmen)n(t)1975 23 y(in)30
b(b)r(oth)g(directions)f(at)h(the)g(same)g(time\).)44
b(W)-7 b(e)30 b(do)g(not)g(kno)n(w)1975 123 y(whether)25
b(Theorem)g(1)g(remains)g(true)h(under)f(this)h(restriction.)1975
262 y Fk(Problem)40 b(2)35 b Fo(Is)h(ther)l(e)h(a)h(p)l(ermutation)e
(of)i(every)g(\014nite)e(set)1975 361 y(of)g(disjoint)g(se)l(gments)f
(such)g(that,)i(extending)e(the)h(se)l(gments)1975 461
y(in)i(b)l(oth)h(dir)l(e)l(ctions)h(in)e(this)h(or)l(der,)k(the)38
b(dual)i(gr)l(aph)f(of)h(the)1975 561 y(r)l(esulting)29
b(c)l(onvex)h(p)l(artition)g(is)g(2-e)l(dge)h(c)l(onne)l(cte)l(d?)1975
824 y Fq(2)91 b(P)m(a)m(rtition)30 b(b)m(y)g(Induction)1975
1020 y Fs(W)-7 b(e)20 b(pro)n(v)n(e)f(Theorem)g(1)h(algorithmically)-7
b(.)33 b(W)-7 b(e)20 b(\014rst)g(sho)n(w)g(that)1975
1119 y(one)25 b(can)f(apply)h(induction)h(in)g(a)f(certain)f(sense.)36
b(It)26 b(is)f(enough)1975 1219 y(to)i(pro)n(v)n(e)f(the)i(follo)n
(wing.)1975 1438 y Fk(Theorem)j(2)41 b Fo(F)-6 b(or)39
b(any)g(\014nite)e(set)h Fp(S)43 b Fo(of)d(disjoint)f(line)g(se)l(g-)
1975 1538 y(ments)j(in)h(the)h(plane,)k(one)43 b(c)l(an)h(\014nd)f(a)g
(nonempty)h(subset)1975 1637 y Fp(S)2031 1607 y Fr(0)2083
1637 y Fh(\022)28 b Fp(S)38 b Fo(and)33 b(c)l(onstruct)f(a)h(c)l(onvex)
g(p)l(artition)h Fp(P)3547 1607 y Fr(0)3603 1637 y Fo(of)g
Fp(S)3760 1607 y Fr(0)3816 1637 y Fo(such)1975 1737 y(that)29
b(the)h(dual)h(gr)l(aph)g(of)f Fp(P)2851 1707 y Fr(0)2904
1737 y Fo(is)h(2-e)l(dge)f(c)l(onne)l(cte)l(d)g(and)g(every)1975
1837 y(se)l(gment)f(of)h Fp(S)23 b Fh(n)18 b Fp(S)2578
1807 y Fr(0)2631 1837 y Fo(lies)31 b(in)e(the)h(interior)h(of)g(a)f
(fac)l(e)g(of)h Fp(P)3827 1807 y Fr(0)3850 1837 y Fo(.)2058
2049 y Fs(Let)24 b(us)h(sho)n(w)e(that)i(Theorem)f(1)g(follo)n(ws)g
(from)g(Theorem)f(2:)1975 2188 y Fk(Pro)s(of)i(of)h(Theorem)g(1.)34
b Fs(Pro)r(ceed)21 b(b)n(y)h(induction)h(on)f Fp(S)5
b Fs(.)35 b(Let)1975 2287 y Fp(S)d Fs(b)r(e)d(a)e(set)h(of)g
Fp(n)g Fs(disjoin)n(t)g(line)g(segmen)n(ts,)f(and)h(assume)f(that)1975
2387 y(an)n(y)j(set)h(of)g(less)f(than)h Fp(n)g Fs(segmen)n(ts)f(has)h
(a)f(con)n(v)n(ex)g(partition)1975 2487 y(whose)f(dual)i(graph)e(is)h
(2-connected.)45 b(By)30 b(Theorem)f(2)h(there)1975 2586
y(is)24 b(a)g(con)n(v)n(ex)g(partition)g Fp(P)2799 2556
y Fr(0)2847 2586 y Fs(of)g(a)h(nonempt)n(y)f(subset)h
Fp(S)3697 2556 y Fr(0)3745 2586 y Fs(of)f(seg-)1975 2686
y(men)n(ts.)46 b(If)32 b Fp(S)h Fs(=)28 b Fp(S)2579 2656
y Fr(0)2602 2686 y Fs(,)k(then)f(the)g(pro)r(of)g(is)f(complete.)47
b(Assume)1975 2785 y(that)22 b Fp(S)11 b Fh(n)c Fp(S)2316
2755 y Fr(0)2361 2785 y Fh(6)p Fs(=)23 b Fh(;)p Fs(.)34
b(By)21 b(induction,)j(the)e(\(p)r(ossibly)f(empt)n(y\))h(sub-)1975
2885 y(set)30 b(of)h(segmen)n(ts)f(lying)h(in)g(eac)n(h)f(face)g
Fp(v)i Fh(2)d Fp(P)3453 2855 y Fr(0)3507 2885 y Fs(has)h(a)h(con)n(v)n
(ex)1975 2985 y(partition)g(\(of)h(that)f(face\))h(whose)f(dual)g
(graph)g Fp(G)p Fs(\()p Fp(v)3661 2955 y Fr(0)3685 2985
y Fs(\))h(is)f(also)1975 3084 y(2-connected.)60 b(The)35
b(partitions)g(of)h(the)g(faces)f(of)g Fp(P)3683 3054
y Fr(0)3742 3084 y Fs(join)n(tly)1975 3184 y(giv)n(e)26
b(a)h(con)n(v)n(ex)g(partition)g Fp(P)39 b Fs(of)28 b
Fp(S)5 b Fs(.)2058 3291 y(The)40 b(dual)g(graph)f Fp(G)i
Fs(of)f Fp(P)52 b Fs(is)40 b(obtained)g(from)g(the)g(dual)1975
3391 y(graph)f Fp(G)2288 3360 y Fr(0)2351 3391 y Fs(of)h
Fp(P)2523 3360 y Fr(0)2587 3391 y Fs(b)n(y)f(replacing)g(eac)n(h)g(v)n
(ertex)g Fp(v)3588 3360 y Fr(0)3656 3391 y Fh(2)44 b
Fp(V)19 b Fs(\()p Fp(G)3919 3360 y Fr(0)3943 3391 y Fs(\))1975
3490 y(with)g(a)f(2-edge)f(connected)i(graph)e Fp(G)p
Fs(\()p Fp(v)3209 3460 y Fr(0)3233 3490 y Fs(\))i(and)g(replacing)e(ev)
n(ery)1975 3590 y(edge)i Fp(u)2204 3560 y Fr(0)2227 3590
y Fp(v)2270 3560 y Fr(0)2316 3590 y Fh(2)24 b Fp(E)5
b Fs(\()p Fp(G)2558 3560 y Fr(0)2581 3590 y Fs(\))20
b(with)h(an)e(edge)g(b)r(et)n(w)n(een)h(some)f(v)n(ertices)f(of)1975
3689 y Fp(G)p Fs(\()p Fp(u)2120 3659 y Fr(0)2143 3689
y Fs(\))29 b(and)f Fp(G)p Fs(\()p Fp(v)2506 3659 y Fr(0)2531
3689 y Fs(\).)40 b(W)-7 b(e)29 b(claim)f(that)h(an)n(y)f(graph)f
Fp(G)i Fs(obtained)1975 3789 y(in)e(this)h(w)n(a)n(y)f(is)g(2-edge)g
(connected.)2058 3896 y(Indeed,)g(it)f(is)h(enough)e(to)i(sho)n(w)e
(that)i(there)f(are)f(t)n(w)n(o)h(edge-)1975 3996 y(disjoin)n(t)31
b(path)h(b)r(et)n(w)n(een)f(an)n(y)g(t)n(w)n(o)f(v)n(ertices,)h
Fp(u)g Fs(and)h Fp(v)s Fs(,)g(of)g Fp(G)p Fs(.)1975 4095
y(This)20 b(is)g(ob)n(vious)f(if)i(b)r(oth)f Fp(u)g Fs(and)g
Fp(v)k Fs(are)19 b(v)n(ertices)g(of)h(a)g(subgraph)1975
4195 y Fp(G)p Fs(\()p Fp(w)2133 4165 y Fr(0)2157 4195
y Fs(\))33 b(corresp)r(onding)d(to)i(some)f(v)n(ertex)g
Fp(w)3395 4165 y Fr(0)3452 4195 y Fs(of)h Fp(G)3616 4165
y Fr(0)3639 4195 y Fs(,)h(b)r(ecause)1975 4294 y Fp(G)p
Fs(\()p Fp(w)2133 4264 y Fr(0)2157 4294 y Fs(\))28 b(is)f(2-edge)f
(connected.)36 b(Assume)28 b(that)f Fp(u)c Fh(2)g Fp(G)p
Fs(\()p Fp(u)3758 4264 y Fr(0)3782 4294 y Fs(\))k(and)1975
4394 y Fp(v)42 b Fh(2)e Fp(G)p Fs(\()p Fp(v)2292 4364
y Fr(0)2316 4394 y Fs(\))e(for)e(t)n(w)n(o)h(distinct)h(no)r(des)f
Fp(u)3290 4364 y Fr(0)3313 4394 y Fp(;)14 b(v)3393 4364
y Fr(0)3456 4394 y Fh(2)39 b Fp(V)19 b Fs(\()p Fp(G)3714
4364 y Fr(0)3738 4394 y Fs(\).)67 b(W)-7 b(e)1975 4494
y(kno)n(w)26 b(that)h Fp(G)2435 4464 y Fr(0)2485 4494
y Fs(is)g(2-edge)e(connected,)i(and)f(so)h(there)f(are)g(t)n(w)n(o)1975
4593 y(edge-disjoin)n(t)g(simple)h(paths)g(b)r(et)n(w)n(een)g
Fp(u)3311 4563 y Fr(0)3361 4593 y Fs(and)g Fp(v)3565
4563 y Fr(0)3615 4593 y Fs(in)g Fp(G)3776 4563 y Fr(0)3800
4593 y Fs(.)37 b(W)-7 b(e)1975 4693 y(extend)27 b(these)g(paths)f(in)n
(to)h(t)n(w)n(o)f(edge-disjoin)n(t)g(path)h(b)r(et)n(w)n(een)1975
4793 y Fp(u)h Fs(and)h Fp(v)j Fs(in)d Fp(G)g Fs(suc)n(h)f(that,)i
(whenev)n(er)d(a)i(path)g(in)g Fp(G)3665 4762 y Fr(0)3717
4793 y Fs(visits)f(a)1975 4892 y(v)n(ertex)f Fp(w)2288
4862 y Fr(0)2337 4892 y Fh(2)e Fp(V)18 b Fs(\()p Fp(G)2580
4862 y Fr(0)2604 4892 y Fs(\),)30 b(w)n(e)e(replace)f
Fp(w)3155 4862 y Fr(0)3208 4892 y Fs(with)i(a)f(path)g(in)h
Fp(G)p Fs(\()p Fp(w)3918 4862 y Fr(0)3943 4892 y Fs(\))1975
4992 y(b)r(et)n(w)n(een)i(the)h(inciden)n(t)g(edges)e(of)i
Fp(E)5 b Fs(\()p Fp(G)3253 4962 y Fr(0)3276 4992 y Fs(\).)49
b(If)32 b(only)f(one)g(path)1975 5091 y(visits)i(a)g(no)r(de)h
Fp(w)2539 5061 y Fr(0)2596 5091 y Fh(2)g Fp(V)19 b Fs(\()p
Fp(G)2849 5061 y Fr(0)2872 5091 y Fs(\),)36 b(then)e(suc)n(h)g(a)f
(path)h(exists)f(b)r(e-)1975 5191 y(cause)18 b Fp(G)p
Fs(\()p Fp(w)2346 5161 y Fr(0)2371 5191 y Fs(\))i(is)f(connected.)34
b(If)20 b(b)r(oth)g(paths)f(visit)g Fp(w)3631 5161 y
Fr(0)3655 5191 y Fs(,)j(then)d(w)n(e)1975 5291 y(connect)31
b(t)n(w)n(o)f(pairs)g(of)h(v)n(ertices)f(in)i Fp(G)p
Fs(\()p Fp(w)3311 5261 y Fr(0)3335 5291 y Fs(\))g(b)n(y)f(edge-disjoin)
n(t)1975 5390 y(paths,)d(whic)n(h)g(can)g(b)r(e)h(done)f(b)r(ecause)g
Fp(G)p Fs(\()p Fp(w)3395 5360 y Fr(0)3419 5390 y Fs(\))h(is)f(2-edge)f
(con-)1975 5490 y(nected.)1677 b Fg(\003)p eop end end
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(of)f(the)i(separator)c(is)j(con)n(v)n(ex.)34 b(W)-7
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r(oin)n(t)g(along)e(the)i(con)n(v)n(ex)e(h)n(ull)-75
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1002 y(an)21 b(extension)394 967 y Fh(\000)-65 b(!)416
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Fp(s)429 2859 y Fi(i)487 2847 y Fh(2)f Fp(S)630 2817
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b(a)g Fo(total)h(turning)f(angle)h Fs(as)e Fp(\015)47
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b(\000)f(!)1598 2958 y Fp(s)1637 2970 y Fi(i)p Fr(\000)p
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Fp(a)877 3370 y Fj(0)914 3358 y Fp(b)950 3370 y Fj(0)1008
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3755 y Fh(\000)-65 b(!)1151 3791 y Fp(r)44 b Fs(un)n(til)20
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Fh(\000)-39 b(\000)f(!)1040 4192 y Fp(a)1084 4204 y Fi(i)1111
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4192 y Fp(r)24 b(;)1735 4134 y Fh(\000)-39 b(\000)g(!)1735
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4252 y Fh(\000)-39 b(\000)g(!)964 4309 y Fp(a)1008 4321
y Fi(i)1036 4309 y Fp(b)1072 4321 y Fi(i)1099 4309 y
Fs(\),)34 b(put)g Fp(S)1402 4279 y Fr(0)1456 4309 y Fs(:=)d
Fp(S)1631 4279 y Fr(0)1676 4309 y Fh([)22 b(f)p Fp(s)1834
4321 y Fi(i)1861 4309 y Fh(g)p Fs(,)274 4409 y Fp(s)h
Fs(:=)f Fp(s)485 4421 y Fi(i)513 4409 y Fs(,)28 b Fp(p)22
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Q
q 0.8 w
0 0 1 RG
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S
q 0 0 1 rg
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Q
Q
q 0.4 w
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Q
q 2 w
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S
Q
q 2 w
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S
Q
q 2 w
153.36 233.988 m
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S
Q
q 2 w
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Q
q 2 w
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S
Q
q 2 w
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q 2 w
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S
Q
q 2 w
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S
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q 2 w
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S
Q
q 2 w
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S
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q 2 w
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S
Q
q 2 w
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S
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q 2 w
52.958 249.231 m
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S
Q
q 2 w
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S
Q
q 2 w
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S
Q
q 2 w
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q 2 w
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S
Q
q 2 w
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S
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S
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q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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35.2306 303.086 34.559 302.414 34.559 301.586 c
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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40.541 262.817 m
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38.2126 264.317 37.541 263.645 37.541 262.817 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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32.588 249.231 m
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30.2596 250.731 29.588 250.059 29.588 249.231 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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54.458 249.231 m
54.458 250.059 53.7864 250.731 52.958 250.731 c
52.1296 250.731 51.458 250.059 51.458 249.231 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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105.487 251.55 m
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103.159 253.05 102.487 252.378 102.487 251.55 c
102.487 250.722 103.159 250.05 103.987 250.05 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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127.743 258.533 m
127.743 259.361 127.072 260.033 126.243 260.033 c
125.415 260.033 124.743 259.361 124.743 258.533 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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124.375 264.473 m
124.375 265.301 123.703 265.973 122.875 265.973 c
122.047 265.973 121.375 265.301 121.375 264.473 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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127.357 277.065 m
127.357 277.893 126.686 278.565 125.857 278.565 c
125.029 278.565 124.357 277.893 124.357 277.065 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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135.641 285.349 m
135.641 286.177 134.97 286.849 134.141 286.849 c
133.313 286.849 132.641 286.177 132.641 285.349 c
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h q f* Q S
Q
q 0.6 w
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142.268 278.059 m
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139.94 279.559 139.268 278.887 139.268 278.059 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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154.86 251.882 m
154.86 252.71 154.189 253.382 153.36 253.382 c
152.532 253.382 151.86 252.71 151.86 251.882 c
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h q f* Q S
Q
q 0.6 w
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154.86 233.988 m
154.86 234.816 154.189 235.488 153.36 235.488 c
152.532 235.488 151.86 234.816 151.86 233.988 c
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154.189 232.488 154.86 233.16 154.86 233.988 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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130.008 229.681 m
130.008 230.509 129.337 231.181 128.508 231.181 c
127.68 231.181 127.008 230.509 127.008 229.681 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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138.955 218.414 m
138.955 219.242 138.283 219.914 137.455 219.914 c
136.626 219.914 135.955 219.242 135.955 218.414 c
135.955 217.586 136.626 216.914 137.455 216.914 c
138.283 216.914 138.955 217.586 138.955 218.414 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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98.86 233.988 m
98.86 234.816 98.1884 235.488 97.36 235.488 c
96.5316 235.488 95.86 234.816 95.86 233.988 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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77.653 228.355 m
77.653 229.183 76.9814 229.855 76.153 229.855 c
75.3246 229.855 74.653 229.183 74.653 228.355 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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109.11 268.329 m
109.11 269.157 108.439 269.829 107.61 269.829 c
106.782 269.829 106.11 269.157 106.11 268.329 c
106.11 267.501 106.782 266.829 107.61 266.829 c
108.439 266.829 109.11 267.501 109.11 268.329 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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97.866 286.675 m
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95.5376 288.175 94.866 287.503 94.866 286.675 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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74.964 318.661 m
74.964 319.489 74.2924 320.161 73.464 320.161 c
72.6356 320.161 71.964 319.489 71.964 318.661 c
71.964 317.833 72.6356 317.161 73.464 317.161 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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106.206 316.176 m
106.206 317.004 105.534 317.676 104.706 317.676 c
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103.206 315.348 103.877 314.676 104.706 314.676 c
105.534 314.676 106.206 315.348 106.206 316.176 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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118.079 305.893 m
118.079 306.721 117.408 307.393 116.579 307.393 c
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115.079 305.065 115.751 304.393 116.579 304.393 c
117.408 304.393 118.079 305.065 118.079 305.893 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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111.452 286.012 m
111.452 286.84 110.78 287.512 109.952 287.512 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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123.712 295.29 m
123.712 296.118 123.041 296.79 122.212 296.79 c
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123.041 293.79 123.712 294.462 123.712 295.29 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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160.493 316.166 m
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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167.783 310.201 m
167.783 311.029 167.112 311.701 166.283 311.701 c
165.455 311.701 164.783 311.029 164.783 310.201 c
164.783 309.373 165.455 308.701 166.283 308.701 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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157.18 339.692 m
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154.851 341.192 154.18 340.52 154.18 339.692 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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146.908 293.302 m
146.908 294.13 146.236 294.802 145.408 294.802 c
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143.908 292.474 144.579 291.802 145.408 291.802 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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131.996 326.106 m
131.996 326.934 131.325 327.606 130.496 327.606 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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143.925 332.402 m
143.925 333.23 143.254 333.902 142.425 333.902 c
141.597 333.902 140.925 333.23 140.925 332.402 c
140.925 331.574 141.597 330.902 142.425 330.902 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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119.405 342.012 m
119.405 342.84 118.733 343.512 117.905 343.512 c
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116.405 341.184 117.076 340.512 117.905 340.512 c
118.733 340.512 119.405 341.184 119.405 342.012 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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165.132 354.272 m
165.132 355.1 164.461 355.772 163.632 355.772 c
162.804 355.772 162.132 355.1 162.132 354.272 c
162.132 353.444 162.804 352.772 163.632 352.772 c
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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167.452 281.704 m
167.452 282.533 166.78 283.204 165.952 283.204 c
165.123 283.204 164.452 282.533 164.452 281.704 c
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h q f* Q S
Q
q 0.4 w
358.621 208.953 m
198.621 208.953 l
198.621 368.953 l
358.621 368.953 l
h S
Q
q 0.4 w
183.308 30.443 m
23.308 30.443 l
23.308 190.443 l
183.308 190.443 l
h S
Q
q 0.4 w
359.308 30.443 m
199.308 30.443 l
199.308 190.443 l
359.308 190.443 l
h S
Q
q 1 0 0 1 209.22 509.492 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(0)]TJ
ET
Q
q 0.4 w
182.62 384.953 m
22.62 384.953 l
22.62 544.953 l
182.62 544.953 l
h S
Q
q 2 w
39.371 531.929 m
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S
Q
q 2 w
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S
Q
q 2 w
153.359 409.988 m
153.359 427.882 l
S
Q
q 2 w
165.951 457.704 m
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S
Q
q 2 w
158.992 492.166 m
122.211 471.29 l
S
Q
q 2 w
116.578 481.893 m
109.951 462.012 l
S
Q
q 2 w
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108.957 442.13 l
S
Q
q 2 w
103.986 427.55 m
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S
Q
q 2 w
166.282 486.201 m
155.679 515.692 l
S
Q
q 2 w
163.632 530.272 m
117.904 518.012 l
S
Q
q 2 w
43.016 456.047 m
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S
Q
q 2 w
52.957 425.231 m
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S
Q
q 2 w
48.649 466.651 m
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S
Q
q 2 w
77.146 520.994 m
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S
Q
q 2 w
142.424 508.402 m
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S
Q
q 2 w
140.767 454.059 m
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S
Q
q 2 w
125.856 453.065 m
122.874 440.473 l
S
Q
q 2 w
128.507 405.681 m
137.454 394.414 l
S
Q
q 0.6 w
1 0 0 RG
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165.132 530.272 m
165.132 531.1 164.46 531.772 163.632 531.772 c
162.803 531.772 162.132 531.1 162.132 530.272 c
162.132 529.444 162.803 528.772 163.632 528.772 c
164.46 528.772 165.132 529.444 165.132 530.272 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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119.404 518.012 m
119.404 518.84 118.732 519.512 117.904 519.512 c
117.076 519.512 116.404 518.84 116.404 518.012 c
116.404 517.184 117.076 516.512 117.904 516.512 c
118.732 516.512 119.404 517.184 119.404 518.012 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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131.995 502.106 m
131.995 502.934 131.324 503.606 130.495 503.606 c
129.667 503.606 128.995 502.934 128.995 502.106 c
128.995 501.278 129.667 500.606 130.495 500.606 c
131.324 500.606 131.995 501.278 131.995 502.106 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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131.995 502.106 m
131.995 502.934 131.324 503.606 130.495 503.606 c
129.667 503.606 128.995 502.934 128.995 502.106 c
128.995 501.278 129.667 500.606 130.495 500.606 c
131.324 500.606 131.995 501.278 131.995 502.106 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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143.924 508.402 m
143.924 509.23 143.253 509.902 142.424 509.902 c
141.596 509.902 140.924 509.23 140.924 508.402 c
140.924 507.574 141.596 506.902 142.424 506.902 c
143.253 506.902 143.924 507.574 143.924 508.402 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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157.179 515.692 m
157.179 516.52 156.507 517.192 155.679 517.192 c
154.85 517.192 154.179 516.52 154.179 515.692 c
154.179 514.864 154.85 514.192 155.679 514.192 c
156.507 514.192 157.179 514.864 157.179 515.692 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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167.782 486.201 m
167.782 487.029 167.111 487.701 166.282 487.701 c
165.454 487.701 164.782 487.029 164.782 486.201 c
164.782 485.373 165.454 484.701 166.282 484.701 c
167.111 484.701 167.782 485.373 167.782 486.201 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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160.492 492.166 m
160.492 492.994 159.821 493.666 158.992 493.666 c
158.164 493.666 157.492 492.994 157.492 492.166 c
157.492 491.338 158.164 490.666 158.992 490.666 c
159.821 490.666 160.492 491.338 160.492 492.166 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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123.711 471.29 m
123.711 472.118 123.04 472.79 122.211 472.79 c
121.383 472.79 120.711 472.118 120.711 471.29 c
120.711 470.462 121.383 469.79 122.211 469.79 c
123.04 469.79 123.711 470.462 123.711 471.29 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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118.078 481.893 m
118.078 482.721 117.407 483.393 116.578 483.393 c
115.75 483.393 115.078 482.721 115.078 481.893 c
115.078 481.065 115.75 480.393 116.578 480.393 c
117.407 480.393 118.078 481.065 118.078 481.893 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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111.451 462.012 m
111.451 462.84 110.779 463.512 109.951 463.512 c
109.122 463.512 108.451 462.84 108.451 462.012 c
108.451 461.184 109.122 460.512 109.951 460.512 c
110.779 460.512 111.451 461.184 111.451 462.012 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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97.865 462.675 m
97.865 463.503 97.1934 464.175 96.365 464.175 c
95.5366 464.175 94.865 463.503 94.865 462.675 c
94.865 461.847 95.5366 461.175 96.365 461.175 c
97.1934 461.175 97.865 461.847 97.865 462.675 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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110.457 442.13 m
110.457 442.958 109.785 443.63 108.957 443.63 c
108.128 443.63 107.457 442.958 107.457 442.13 c
107.457 441.302 108.128 440.63 108.957 440.63 c
109.785 440.63 110.457 441.302 110.457 442.13 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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105.486 427.55 m
105.486 428.378 104.814 429.05 103.986 429.05 c
103.158 429.05 102.486 428.378 102.486 427.55 c
102.486 426.722 103.158 426.05 103.986 426.05 c
104.814 426.05 105.486 426.722 105.486 427.55 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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129.344 435.172 m
129.344 436 128.673 436.672 127.844 436.672 c
127.016 436.672 126.344 436 126.344 435.172 c
126.344 434.344 127.016 433.672 127.844 433.672 c
128.673 433.672 129.344 434.344 129.344 435.172 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
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124.374 440.473 m
124.374 441.301 123.702 441.973 122.874 441.973 c
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Q
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Q
q 0.6 w
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Q
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Q
q 0.6 w
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Q
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Q
q 0.6 w
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Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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Q
q 2 w
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S
Q
q 0.6 w
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284.843 137.51 m
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Q
q 0.8 w
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S
q 1 0 0 rg
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h q f* Q S
Q
Q
q 0.8 w
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S
q 0 0 1 rg
52.844 141.844 m
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
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S
q 0 0 1 rg
85.009 52.015 m
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h q f* Q S
Q
Q
q 0.8 w
1 0 0 RG
110.639 107.502 m
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S
q 1 0 0 rg
130.123 165.247 m
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h q f* Q S
Q
Q
q 0.8 w
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126.93 80.023 m
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S
q 1 0 0 rg
80.373 64.954 m
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
108.596 74.293 m
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S
q 0 0 1 rg
154.394 88.606 m
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
99.482 104.202 m
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S
q 0 0 1 rg
117.061 76.997 m
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
115.908 123.308 m
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S
q 0 0 1 rg
105.849 93.813 m
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
148.599 131.366 m
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S
q 0 0 1 rg
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114.873 111.466 l
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
163.81 104.791 m
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S
q 0 0 1 rg
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h q f* Q S
Q
Q
q 0.8 w
0 0 1 RG
154.047 59.123 m
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S
q 0 0 1 rg
154.646 109.964 m
153.611 106.976 l
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h q f* Q S
Q
Q
q 0.8 w
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S
q 0 0 1 rg
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Q
Q
q 2 w
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S
Q
q 2 w
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q 2 w
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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h q f* Q S
Q
q 0.6 w
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Q
q 0.6 w
1 0 0 RG
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Q
q 0.6 w
1 0 0 RG
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h q f* Q S
Q
q 0.6 w
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Q
q 0.6 w
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Q
q 0.6 w
1 0 0 RG
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Q
q 0.6 w
1 0 0 RG
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Q
q 0.6 w
1 0 0 RG
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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137.313 41.404 136.642 40.7324 136.642 39.904 c
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
1 0 0 RG
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78.34 50.6734 77.6684 51.345 76.84 51.345 c
76.0116 51.345 75.34 50.6734 75.34 49.845 c
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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98.553 108.165 m
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96.2246 109.665 95.553 108.993 95.553 108.165 c
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h q f* Q S
Q
q 0.6 w
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h q f* Q S
Q
q 0.6 w
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75.651 140.151 m
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73.3226 141.651 72.651 140.979 72.651 140.151 c
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h q f* Q S
Q
q 0.6 w
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118.766 127.383 m
118.766 128.211 118.095 128.883 117.266 128.883 c
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118.095 125.883 118.766 126.555 118.766 127.383 c
h q f* Q S
Q
q 0.6 w
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112.139 107.502 m
112.139 108.33 111.467 109.002 110.639 109.002 c
109.81 109.002 109.139 108.33 109.139 107.502 c
109.139 106.674 109.81 106.002 110.639 106.002 c
111.467 106.002 112.139 106.674 112.139 107.502 c
h q f* Q S
Q
q 0.6 w
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124.399 116.78 m
124.399 117.608 123.728 118.28 122.899 118.28 c
122.071 118.28 121.399 117.608 121.399 116.78 c
121.399 115.952 122.071 115.28 122.899 115.28 c
123.728 115.28 124.399 115.952 124.399 116.78 c
h q f* Q S
Q
q 0.6 w
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161.18 137.656 m
161.18 138.484 160.509 139.156 159.68 139.156 c
158.852 139.156 158.18 138.484 158.18 137.656 c
158.18 136.828 158.852 136.156 159.68 136.156 c
160.509 136.156 161.18 136.828 161.18 137.656 c
h q f* Q S
Q
q 0.6 w
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168.47 131.691 m
168.47 132.519 167.799 133.191 166.97 133.191 c
166.142 133.191 165.47 132.519 165.47 131.691 c
165.47 130.863 166.142 130.191 166.97 130.191 c
167.799 130.191 168.47 130.863 168.47 131.691 c
h q f* Q S
Q
q 0.6 w
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157.867 161.182 m
157.867 162.01 157.195 162.682 156.367 162.682 c
155.538 162.682 154.867 162.01 154.867 161.182 c
154.867 160.354 155.538 159.682 156.367 159.682 c
157.195 159.682 157.867 160.354 157.867 161.182 c
h q f* Q S
Q
q 0.6 w
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147.595 114.792 m
147.595 115.62 146.923 116.292 146.095 116.292 c
145.266 116.292 144.595 115.62 144.595 114.792 c
144.595 113.964 145.266 113.292 146.095 113.292 c
146.923 113.292 147.595 113.964 147.595 114.792 c
h q f* Q S
Q
q 0.6 w
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132.683 147.596 m
132.683 148.424 132.012 149.096 131.183 149.096 c
130.355 149.096 129.683 148.424 129.683 147.596 c
129.683 146.768 130.355 146.096 131.183 146.096 c
132.012 146.096 132.683 146.768 132.683 147.596 c
h q f* Q S
Q
q 0.6 w
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144.612 153.892 m
144.612 154.72 143.941 155.392 143.112 155.392 c
142.284 155.392 141.612 154.72 141.612 153.892 c
141.612 153.064 142.284 152.392 143.112 152.392 c
143.941 152.392 144.612 153.064 144.612 153.892 c
h q f* Q S
Q
q 0.6 w
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118.035 146.38 m
118.035 147.208 117.363 147.88 116.535 147.88 c
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115.035 145.552 115.706 144.88 116.535 144.88 c
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h q f* Q S
Q
q 0.6 w
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120.092 163.502 m
120.092 164.33 119.42 165.002 118.592 165.002 c
117.763 165.002 117.092 164.33 117.092 163.502 c
117.092 162.674 117.763 162.002 118.592 162.002 c
119.42 162.002 120.092 162.674 120.092 163.502 c
h q f* Q S
Q
q 0.6 w
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165.819 175.762 m
165.819 176.59 165.148 177.262 164.319 177.262 c
163.491 177.262 162.819 176.59 162.819 175.762 c
162.819 174.934 163.491 174.262 164.319 174.262 c
165.148 174.262 165.819 174.934 165.819 175.762 c
h q f* Q S
Q
q 0.6 w
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168.139 103.194 m
168.139 104.022 167.467 104.694 166.639 104.694 c
165.81 104.694 165.139 104.022 165.139 103.194 c
165.139 102.366 165.81 101.694 166.639 101.694 c
167.467 101.694 168.139 102.366 168.139 103.194 c
h q f* Q S
Q
q 2 w
105.392 137.666 m
105.392 137.666 l
72.201 140.307 l
S
Q
q 0.6 w
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75.651 140.151 m
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73.3226 141.651 72.651 140.979 72.651 140.151 c
72.651 139.323 73.3226 138.651 74.151 138.651 c
74.9794 138.651 75.651 139.323 75.651 140.151 c
h q f* Q S
Q
q 0.6 w
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106.893 137.666 m
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Q
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Q
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Q
Q
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S
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Q
Q
q 0.8 w
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S
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Q
Q
q 0.8 w
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S
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Q
Q
q 0.8 w
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Q
Q
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S
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Q
Q
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S
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Q
Q
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Q
q 0.6 w
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Q
q 0.6 w
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Q
q 0.6 w
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Q
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Q
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Q
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Q
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Q
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Q
q 0.6 w
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Q
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Q
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Q
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Q
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Q
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Q
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Q
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Q
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Q
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Q
q 0.6 w
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Q
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Q
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Q
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BT
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ET
Q
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Q
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Q
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BT
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ET
Q
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BT
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ET
Q
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BT
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ET
Q
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BT
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ET
Q
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BT
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ET
Q
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BT
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ET
Q
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(6)]TJ
ET
Q
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(7)]TJ
ET
Q
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BT
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ET
Q
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(3)]TJ
ET
Q
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 100.632 288.105 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 97.477 262.428 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 129.152 252.409 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 32.813 333.085 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 27.003 350.81 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 94.006 225.041 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 64.77 223.166 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 149.583 223.214 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
1 0 0 1 0 -785.773 cm
BT
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ET
Q
q 1 0 0 1 167.495 276.571 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(3)]TJ
ET
Q
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0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 113.062 307.779 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 85.047 284.419 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 100.946 241.891 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
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BT
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ET
Q
q 1 0 0 1 331.249 248.551 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(2)]TJ
ET
Q
q 1 0 0 1 318.565 296.172 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 297.302 287.496 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 275.826 287.479 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 273.406 262.906 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 305.081 252.887 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 208.742 333.563 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 202.932 351.288 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(0)]TJ
ET
Q
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0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 240.699 223.644 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(1)]TJ
ET
Q
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0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(2)]TJ
ET
Q
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0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 324.729 316.976 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 288.991 308.257 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 260.976 284.897 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 275.919 241.892 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 155.798 69.275 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(2)]TJ
ET
Q
q 1 0 0 1 143.114 116.896 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 119.785 108.758 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 101.11 110.41 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 97.955 83.63 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 129.63 73.611 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 33.291 154.287 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 27.481 172.012 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 96.007 47.549 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 65.248 44.368 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
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0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 156.806 50.074 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(2)]TJ
ET
Q
q 1 0 0 1 167.973 97.773 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 150.418 138.135 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 106.914 125.297 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 86.628 103.415 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 99.996 63.611 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 331.988 71.451 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(2)]TJ
ET
Q
q 1 0 0 1 319.521 116.896 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 296.793 108.908 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 274.362 83.63 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 306.037 73.611 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 212.962 155.593 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 205.847 172.012 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
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BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(0)]TJ
ET
Q
q 1 0 0 1 270.891 46.243 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 249.489 40.234 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(1)]TJ
ET
Q
q 1 0 0 1 332.779 50.509 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(2)]TJ
ET
Q
q 1 0 0 1 340.463 105.389 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(3)]TJ
ET
Q
q 1 0 0 1 324.582 137.7 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(4)]TJ
ET
Q
q 1 0 0 1 263.238 104.968 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(6)]TJ
ET
Q
q 1 0 0 1 276.839 64.264 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(7)]TJ
ET
Q
q 1 0 0 1 244.844 321.251 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(8)]TJ
ET
Q
q 1 0 0 1 278.309 318.861 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(8)]TJ
ET
Q
q 1 0 0 1 69.393 142.453 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(8)]TJ
ET
Q
q 1 0 0 1 102.858 140.063 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(8)]TJ
ET
Q
q 1 0 0 1 247.713 142.453 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(8)]TJ
ET
Q
q 1 0 0 1 279.219 139.628 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(8)]TJ
ET
Q
q 0.6 w
1 0 0 RG
1 0 0 rg
251.651 140.151 m
251.651 140.979 250.979 141.651 250.151 141.651 c
249.323 141.651 248.651 140.979 248.651 140.151 c
248.651 139.323 249.323 138.651 250.151 138.651 c
250.979 138.651 251.651 139.323 251.651 140.151 c
h q f* Q S
Q
q 0.8 w
0 0 1 RG
291.908 123.308 m
281.849 93.813 l
S
q 0 0 1 rg
281.849 93.813 m
283.764 96.3297 l
281.871 96.9752 l
h q f* Q S
Q
Q
q 2 w
293.266 127.383 m
286.639 107.502 l
S
Q
q 0.6 w
1 0 0 RG
1 0 0 rg
294.766 127.383 m
294.766 128.211 294.095 128.883 293.266 128.883 c
292.438 128.883 291.766 128.211 291.766 127.383 c
291.766 126.555 292.438 125.883 293.266 125.883 c
294.095 125.883 294.766 126.555 294.766 127.383 c
h q f* Q S
Q
q 0.6 w
1 0 0 RG
1 0 0 rg
288.139 107.502 m
288.139 108.33 287.467 109.002 286.639 109.002 c
285.81 109.002 285.139 108.33 285.139 107.502 c
285.139 106.674 285.81 106.002 286.639 106.002 c
287.467 106.002 288.139 106.674 288.139 107.502 c
h q f* Q S
Q
q 1 0 0 1 276.85 110.379 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 283.187 126.1 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(5)]TJ
ET
Q
q 1 0 0 1 335.626 161.241 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(10)]TJ
ET
Q
q 1 0 0 1 346.092 129.233 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(10)]TJ
ET
Q
q 1 0 0 1 114.174 166.496 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -788.139 cm
BT
/F17 8.966 Tf 0 788.139 Td[(a)]TJ/F16 5.978 Tf 4.882 -0.996 Td[(9)]TJ
ET
Q
q 1 0 0 1 166.557 177.095 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(9)]TJ
ET
Q
q 1 0 0 1 336.823 178.198 cm 1 0 0 1 0 0 cm 1 0 0 1 0 0.996 cm
0 g
0 G
1 0 0 1 0 -785.773 cm
BT
/F17 8.966 Tf 0 785.773 Td[(b)]TJ/F16 5.978 Tf 3.949 -0.996 Td[(9)]TJ
ET
Q
q 2 w
292.535 146.38 m
280.274 154.333 l
S
Q
q 0.6 w
1 0 0 RG
1 0 0 rg
281.774 154.333 m
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@endspecial 1975 983 a Fs(Figure)39 b(5:)62 b(The)40
b(b)r(oundary)g(of)g(ev)n(ery)f(region)g(in)i Fh(R)f
Fs(either)1975 1083 y(con)n(tains)f(an)i(en)n(tire)f(segmen)n(t)g
(\(e.g.,)k(face)c Fp(A)p Fs(\))h(or)f(con)n(tains)1975
1182 y(extensions)27 b(of)g(the)h(same)f(orien)n(tation)f(\()p
Fp(B)t Fs(,)i Fp(C)6 b Fs(,)29 b(and)e Fp(A)19 b Fh([)f
Fp(B)t Fs(\).)1975 1452 y(segmen)n(t)23 b(insertions)h(can)f(b)r(e)i
(done)f(in)g Fp(O)r Fs(\(\()p Fp(n)3389 1422 y Fj(2)3428
1452 y Fp(=)3470 1381 y Fh(p)p 3538 1381 46 4 v 3538
1452 a Fp(k)s Fs(\))14 b(log)3738 1415 y Fi(O)r Fj(\(1\))3893
1452 y Fp(n)p Fs(\))1975 1552 y(time)23 b(using)g Fp(O)r
Fs(\()p Fp(k)2515 1522 y Fj(1+)p Fi(")2636 1552 y Fs(\))h(space)e(and)h
(prepro)r(cessing,)g(where)g Fp(n)f Fh(\024)1975 1651
y Fp(k)27 b Fh(\024)d Fp(n)2184 1621 y Fj(2)2249 1651
y Fs(is)k(a)g(parameter)f(and)h Fp(")c(>)g Fs(0)k(is)g(an)g
(arbitrarily)e(small)1975 1751 y(p)r(ositiv)n(e)h(constan)n(t)g([1)o(,)
h(2)o(,)g(4].)2058 1851 y(With)37 b Fp(k)k Fs(=)d Fp(n)2518
1820 y Fj(4)p Fi(=)p Fj(3)2622 1851 y Fs(,)h(our)d(algorithm)f(can)h(b)
r(e)h(implemen)n(ted)1975 1950 y(in)f Fp(O)r Fs(\()p
Fp(n)2227 1920 y Fj(4)p Fi(=)p Fj(3+)p Fi(")2414 1950
y Fs(\))g(time)h(and)e(space;)40 b(with)c Fp(k)k Fs(=)c
Fp(n)p Fs(,)i(it)e(requires)1975 2050 y Fp(O)r Fs(\()p
Fp(n)2122 2020 y Fj(1+)p Fi(")2242 2050 y Fs(\))28 b(space)f(and)g
Fp(O)r Fs(\()p Fp(n)2832 2020 y Fj(3)p Fi(=)p Fj(2)2960
2050 y Fs(p)r(olylog)14 b Fp(n)p Fs(\))28 b(time.)1975
2250 y Fq(References)2010 2394 y Fm([1])41 b(P)-6 b(.)29
b(K.)f(Agarw)n(al)h(and)h(J.)e(Eric)n(kson,)j(Geometric)f(range)f
(searc)n(hing)2126 2473 y(and)19 b(its)f(relativ)n(es,)h(in)f
Fb(A)l(dvanc)l(es)j(in)g(Discr)l(ete)e(and)j(Computational)2126
2552 y(Ge)l(ometry)p Fm(,)38 b(v)n(ol.)d(223)h(of)f(Con)n(temp)r(orary)
i(Mathematics,)i(AMS,)2126 2631 y(1999,)24 b(pp.)g(1-56.)2010
2743 y([2])41 b(P)-6 b(.)49 b(K.)g(Agarw)n(al)g(and)i(M.)d(Sharir,)55
b(Applications)50 b(of)g(a)f(new)2126 2822 y(space)22
b(partitioning)h(tec)n(hnique,)g Fb(Discr)l(ete)g(Comput.)h(Ge)l(om.)f
Fa(9)e Fm(\(1\))2126 2901 y(\(1993\),)k(11{38.)2010 3013
y([3])41 b(O.)23 b(Aic)n(hholzer,)h(S.)f(Bereg,)h(A.)f(Dumitrescu,)h
(A.)f(Garc)-8 b(\023)-27 b(\020a,)24 b(C.)f(Hue-)2126
3092 y(mer,)34 b(F.)f(Hurtado,)i(M.)d(Kano,)k(A.)c(M\023)-35
b(arquez,)35 b(S.)e(Smoro)r(dinsky)-6 b(,)2126 3170 y(D.)26
b(Souv)l(aine,)i(J.)e(Urrutia,)f(and)i(D.)f(R.)g(W)-6
b(o)r(o)r(d,)28 b(Compatible)f(geo-)2126 3249 y(metric)d(matc)n(hings,)
g(in)f(preparation.)2010 3361 y([4])41 b(S.)25 b(W.)g(Cheng)h(and)f(R.)
g(Janardan,)h(Algorithms)e(for)g(ra)n(y-sho)r(oting)2126
3440 y(and)34 b(in)n(tersection)h(searc)n(hing,)h Fb(J.)f(A)n
(lgorithms)f Fa(13)f Fm(\(1992\),)38 b(670{)2126 3519
y(692.)2010 3631 y([5])j(M.)36 b(Ho\013mann,)42 b(B.)37
b(Sp)r(ec)n(kmann,)42 b(and)c(Cs.)f(D.)g(T\023)-35 b(oth,)41
b(P)n(oin)n(ted)2126 3710 y(binary)35 b(encompassing)i(trees:)55
b(simple)35 b(and)h(optimal,)i Fb(Comput.)2126 3789 y(Ge)l(om.)26
b(The)l(ory)h(Appl.)d Fm(\(2007\),)h(to)f(app)r(ear.)2010
3901 y([6])41 b(Z.)32 b(Jin,)j(M.)d(Kano,)j(X.)d(Li,)i(and)g(B.)e(W)-6
b(ei,)35 b(P)n(artitioning)e(2-edge-)2126 3980 y(colored)38
b(complete)g(m)n(ultipartite)g(graphs)g(in)n(to)g(mono)r(c)n(hromatic)
2126 4059 y(cycles,)20 b(paths)g(and)g(trees,)g Fb(J.)i(Comb.)g(Optim.)
d Fa(11)f Fm(\(4\))i(\(2006\),)i(445{)2126 4138 y(454.)2010
4250 y([7])41 b(A.)21 b(Kanek)n(o)h(and)g(M.)f(Kano,)g(Discrete)h
(geometry)h(on)e(red)h(and)g(blue)2126 4329 y(p)r(oin)n(ts)e(in)f(the)i
(plane|a)e(surv)n(ey)-6 b(,)21 b(in)e Fb(Discr)l(ete)i(and)i(c)l
(omputational)2126 4407 y(ge)l(ometry)p Fm(,)29 b(v)n(ol.)g(25)g(of)g
(Algorithms)f(Com)n(bin.,)i(Springer,)f(Berlin,)2126
4486 y(2003,)24 b(pp.)g(551{570.)2010 4598 y([8])41 b(J.)21
b(O'Rourk)n(e,)g Fb(A)n(rt)j(Gal)t(lery)f(The)l(or)l(ems)j(and)e(A)n
(lgorithms)p Fm(,)e(Oxford)2126 4677 y(Univ)n(ersit)n(y)h(Press,)g
(1987.)2010 4789 y([9])41 b(Cs.)20 b(D.)g(T\023)-35 b(oth,)22
b(Illumination)f(in)g(the)h(presence)f(of)g(opaque)h(line)f(seg-)2126
4868 y(men)n(ts)34 b(in)e(the)i(plane,)i Fb(Comput.)f(Ge)l(om.)h(The)l
(ory)f(Appl.)e Fa(21)g Fm(\(3\))2126 4947 y(\(2002\),)25
b(193{204.)1975 5059 y([10])41 b(Cs.)18 b(D.)g(T\023)-35
b(oth,)21 b(Illuminating)e(disjoin)n(t)g(line)f(segmen)n(ts)i(in)f(the)
h(plane,)2126 5138 y Fb(Discr)l(ete)25 b(Comput.)h(Ge)l(om.)f
Fa(30)d Fm(\(3\))j(\(2003\),)g(489{505.)1975 5250 y([11])41
b(J.)24 b(Urrutia,)g(Art)g(gallery)g(and)h(illumination)f(problems,)g
(in)h Fb(Hand-)2126 5329 y(b)l(o)l(ok)34 b(of)f(Computational)j(Ge)l
(ometry)d(\(Eds.)h(J.-R.)f(Sack)g(and)h(J.)2126 5408
y(Urrutia\))p Fm(,)23 b(Amsterdam,)h(North-Holland,)f(2000,)h(pp.)f
(973{1027.)p eop end end
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userdict /end-hook known{end-hook}if
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