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
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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 -