Sign-solvable linear complementarity problems

Naonori Kakimura

Sign-solvable linear complementarity problems

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings
Pages	397-409
Number of pages	13
Publication status	Published - 2007 Dec 1
Externally published	Yes
Event	12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII - Ithaca, NY, United States Duration: 2007 Jun 25 → 2007 Jun 27

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4513 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII
Country	United States
City	Ithaca, NY
Period	07/6/25 → 07/6/27

Keywords

Combinatorial matrix theory
Linear complementarity problems

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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Cite this

Sign-solvable linear complementarity problems. / Kakimura, Naonori.

Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings. 2007. p. 397-409 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4513 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kakimura, N 2007, Sign-solvable linear complementarity problems. in Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4513 LNCS, pp. 397-409, 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII, Ithaca, NY, United States, 07/6/25.

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