TY - GEN

T1 - Sign-solvable linear complementarity problems

AU - Kakimura, Naonori

N1 - Funding Information:
The author is very obliged to Satoru Iwata for his suggestions and reading the draft of the paper. This work is supported by the 21st Century COE Program on Information Science and Technology Strategic Core at the University of Tokyo from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Combinatorial matrix theory

KW - Linear complementarity problems

UR - http://www.scopus.com/inward/record.url?scp=38049029096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049029096&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72792-7_30

DO - 10.1007/978-3-540-72792-7_30

M3 - Conference contribution

AN - SCOPUS:38049029096

SN - 9783540727910

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 397

EP - 409

BT - Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings

PB - Springer Verlag

T2 - 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII

Y2 - 25 June 2007 through 27 June 2007

ER -