Parameterized complexity of sparse linear complementarity problems

Hanna Sumita, Naonori Kakimura, Kazuhisa Makino

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study the parameterized complexity of the linear complementarity problem (LCP), which is one of the most fundamental mathematical optimization problems. The parameters we focus on are the sparsities of the input and the output of the LCP: the maximum numbers of nonzero entries per row/column in the coefficient matrix and the number of nonzero entries in a solution. Our main result is to present a fixed-parameter algorithm for the LCP with all the parameters. We also show that if we drop any of the three parameters, then the LCP is fixed-parameter intractable. In addition, we discuss the nonexistence of a polynomial kernel for the LCP.

Original languageEnglish
Title of host publication10th International Symposium on Parameterized and Exact Computation, IPEC 2015
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages355-364
Number of pages10
Volume43
ISBN (Electronic)9783939897927
DOIs
Publication statusPublished - 2015 Nov 1
Externally publishedYes
Event10th International Symposium on Parameterized and Exact Computation, IPEC 2015 - Patras, Greece
Duration: 2015 Sep 162015 Sep 18

Other

Other10th International Symposium on Parameterized and Exact Computation, IPEC 2015
CountryGreece
CityPatras
Period15/9/1615/9/18

Keywords

  • Linear complementarity problem
  • Parameterized complexity
  • Sparsity

ASJC Scopus subject areas

  • Software

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  • Cite this

    Sumita, H., Kakimura, N., & Makino, K. (2015). Parameterized complexity of sparse linear complementarity problems. In 10th International Symposium on Parameterized and Exact Computation, IPEC 2015 (Vol. 43, pp. 355-364). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.IPEC.2015.355