Sign-Solvable Linear Complementarity Problems

Authors:
Naonori Kakimura
Affiliations:
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
Venue:
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Year:
2007

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Abstract

This paper presents a connection between qualitative matrix theory and linear complementarity problems (LCPs). An LCP is said to be sign-solvableif 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(茂戮驴) time, where 茂戮驴is the number of the nonzero coefficients.