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Sample session with cdd+

With cdd+ and any reasonable LP code, the only necessary step should be to prepare the LP file for determination of the Delaunay cell containing a given point $ c\in R^d$. Consider the same example 3.4.1.

For a given point $ c = (3, 2)$, the LP (11) file for cdd+ is


H-representation
begin
  6  4  rational
  0  1  0  0
  5  1  2  1
  5  1  1  2
 16  1  4  0
 16  1  0  4
 32  1  4  4
end
minimize
  0  1  3  2


The solution by cddr+ is:


*LP status: a dual pair (x, y) of optimal solutions found.
begin
  primal_solution
  1 :  14
  2 :  -15/2
  3 :  -4
  dual_solution
  4 :  -1/8
  2 :  -1/2
  6 :  -3/8
  optimal_value : -33/2
end


Therefore, the facet inequality is $ 14 - 15/2 x_1 - 4 x_2 \ge 0$, and the dual solution indicate that the points $ p^2, p^4, p^6$ determine the Delaunay cell which contains $ (3, 2)$.



Komei Fukuda 2004-08-26