Publication

Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron

Thomas Liebling, François Margot
1994
Report or working paper
Abstract

In this paper, we investigate the applicability of backtrack technique for solving the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is apolynomial in the input size, but the vertex enumeration problem requires a backtrack algorithm to solve a decision problem, called the restricted vertex problem, for each output, which is shown to be NP-complete. Some related NP-complete problems associated with a system of linear inequalities are also discussed, including the optimal vertex problems for polyhedra and arrangements of hyperplanes.

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