License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2015.355
URN: urn:nbn:de:0030-drops-55962
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5596/
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Sumita, Hanna ; Kakimura, Naonori ; Makino, Kazuhisa

Parameterized Complexity of Sparse Linear Complementarity Problems

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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.

BibTeX - Entry

@InProceedings{sumita_et_al:LIPIcs:2015:5596,
  author =	{Hanna Sumita and Naonori Kakimura and Kazuhisa Makino},
  title =	{{Parameterized Complexity of Sparse Linear Complementarity Problems}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{355--364},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5596},
  URN =		{urn:nbn:de:0030-drops-55962},
  doi =		{10.4230/LIPIcs.IPEC.2015.355},
  annote =	{Keywords: linear complementarity problem, sparsity, parameterized complexity}
}

Keywords: linear complementarity problem, sparsity, parameterized complexity
Collection: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 19.11.2015


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