Sign-solvable linear complementarity problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a connection between qualitative matrix theory and linear complementarity problems (LCPs). An LCP is said to be sign-solvable if the set of the sign patterns of the solutions is uniquely determined by the sign patterns of the given coefficients. We provide a characterization for sign-solvable LCPs such that the coefficient matrix has nonzero diagonals, which can be tested in polynomial time. This characterization leads to an efficient combinatorial algorithm to find the sign pattern of a solution for these LCPs. The algorithm runs in O(γ) time, where γ is the number of the nonzero coefficients.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings
Pages397-409
Number of pages13
Publication statusPublished - 2007 Dec 1
Externally publishedYes
Event12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII - Ithaca, NY, United States
Duration: 2007 Jun 252007 Jun 27

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4513 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII
CountryUnited States
CityIthaca, NY
Period07/6/2507/6/27

Keywords

  • Combinatorial matrix theory
  • Linear complementarity problems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kakimura, N. (2007). Sign-solvable linear complementarity problems. In Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings (pp. 397-409). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4513 LNCS).