Sparse linear complementarity problems

Hanna Sumita, Naonori Kakimura, Kazuhisa Makino

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

In this paper, we study the sparse linear complementarity problem, denoted by k-LCP: the coefficient matrix has at most k nonzero entries per row. It is known that 1-LCP is solvable in linear time, while 3-LCP is strongly NP-hard. We show that 2-LCP is strongly NP-hard, while it can be solved in O(n3 logn) time if it is sign-balanced, i.e., each row has at most one positive and one negative entries, where n is the number of constraints. Our second result matches with the currently best known complexity bound for the corresponding sparse linear feasibility problem. In addition, we show that an integer variant of sign-balanced 2-LCP is weakly NP-hard and pseudo-polynomially solvable, and the generalized 1-LCP is strongly NP-hard.

本文言語English
ホスト出版物のタイトルAlgorithms and Complexity - 8th International Conference, CIAC 2013, Proceedings
ページ358-369
ページ数12
DOI
出版ステータスPublished - 2013 9 9
外部発表はい
イベント8th International Conference on Algorithms and Complexity, CIAC 2013 - Barcelona, Spain
継続期間: 2013 5 222013 5 24

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7878 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other8th International Conference on Algorithms and Complexity, CIAC 2013
CountrySpain
CityBarcelona
Period13/5/2213/5/24

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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