Komei Fukuda's Home Page

A dual pair of polytopes

fukuda@ifor.math.ethz.ch (at ETHZ)
komei.fukuda@epfl.ch (at EPFL)
Addresses and Phones
Institute for Operations Research ( Dept. of Math.)
ETH Zentrum, CH-8092 Zurich, Switzerland

tel +41-1-632.4023; fax +41-1-632.1025
Dept. of Mathematics
EPFL, CH-1015 Lausanne, Switzerland
tel +41-21-693.2536; fax +41-21-693.5570

Link to my official page at ETHZ
I also work for Theory of Combinatorial Algorithms Group of Prof. Emo Welzl

Hot News

Polytope Movie Page (Just for Fun)
Click here for a show. Hopefully I will have time to extend it...
Colloquium on Combinatorics, Geometry and Computation
Homepage .
A Joint Ph.D. Program "Combinatorics, Geomery and Computation" of ETHZ and Berlin universities.
Applications for the Predoc-Program.
Polyhedral Computation FAQ
This is an FAQ of geometric computation, focused on Convex Hull, Vertex Enumeration, Voronoi Diagram, Delaunay Triangulation computation in general dimensions. Two versions: html version or pdf file.

Updates of Polyhedral Computation Codes
David Avis has released a new lrs version 3.2 with users' guide in html, see lrs homepage.
I have just updated cdd+ (to ver.076a), see cdd homepage. A new callable library version of cdd has been released on March 9, 2001 as cddlib-091d which can be used as a standalone program and can run in floating point arithmetic with both C double and in rational arithmetic with GMP rational.
International Congress of Mathematical Software, 2002
A Satellite Conference of ICM 2002, Beijing, August 17-19, 2002. call for papers.

Older Links

Strange Unfoldings of Convex Polytopes
Some interesting unfoldings against human intuition. Click here for ingenious examples by M. Namiki, T. Matsui and G. Rote.

Research Activities

Polyhedra Project
This is a joint project with David Avis of McGill University, Canada. It is to develop efficient algorithms and computer programs to compute all vertices of a given convex polyhedron P = { x : A x <= b}, for a given real/rational matrix A and a vector b. There are two codes available, the reverse search code lrs by Avis and the double description code cdd by Fukuda, from the following sites. Note that lrs is efficient for nondegenerate or slightly degenerate inputs and cdd is efficient for highly degenerate inputs.
Mathematica Codes for Convex Polytopes
UnfoldPolytopes, VertexEnum, TriEnum etc.

ETHZ-EPFL Joint Research Project on Optimization and Geometric Computation
This is a joint project with Click here for its homepage. The main goal of the project is to combine the most advanced technology of optimization and geometric computation, and to develop new state-of-the-art theory, techniques and software. The project started September 1996 and the research subjects being investigated include:
Recent Papers

This page is written by Komei Fukuda (ETH Zurich, Switzerland) homepage, e-mail.
Last updated: June 23, 2002