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

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.

    Note:

    PRO 94.07

    Reference

    • ROSO-REPORT-1994-001

    Record created on 2006-02-13, modified on 2016-08-08

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