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

Abstract

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 polynomial 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.

Authors:
; ;
Publication Date:
OSTI Identifier:
36262
Report Number(s):
CONF-9408161-
TRN: 94:009753-0588
Resource Type:
Conference
Resource Relation:
Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; MATRICES; NUMERICAL SOLUTION; EFFICIENCY; ALGORITHMS; LINEAR PROGRAMMING

Citation Formats

Margot, F, Fukuda, K, and Liebling, T. Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron. United States: N. p., 1994. Web.
Margot, F, Fukuda, K, & Liebling, T. Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron. United States.
Margot, F, Fukuda, K, and Liebling, T. 1994. "Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron". United States.
@article{osti_36262,
title = {Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron},
author = {Margot, F and Fukuda, K and Liebling, T},
abstractNote = {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 polynomial 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.},
doi = {},
url = {https://www.osti.gov/biblio/36262}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Dec 31 00:00:00 EST 1994},
month = {Sat Dec 31 00:00:00 EST 1994}
}

Conference:
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