### 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 |
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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) |
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Volume | 4513 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII |
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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

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).