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Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices

Authors Khaled Elbassioni, Kazuhisa Makino

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Author Details

Khaled Elbassioni
  • Masdar Institute, Khalifa University of Science and Technology, Abu Dhabi 54224, UAE
Kazuhisa Makino
  • Research Institute for Mathematical Sciences (RIMS) Kyoto University, Kyoto 606-8502, Japan

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Khaled Elbassioni and Kazuhisa Makino. Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SWAT.2018.18

Abstract

We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron P=P(A,1_)={x in R^n | Ax >= 1_, x >= 0_}, when A is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour's decomposition of totally unimodular matrices, and may be of independent interest.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Hypergraphs
Keywords
  • Totally unimodular matrices
  • Vertices of polyhedra
  • Vertex enumeration
  • Hypergraph transversals
  • Hypergraph decomposition
  • Output polynomial-time algorithm

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