Parameterized Complexity of Sparse Linear Complementarity Problems

Hanna Sumita, Naonori Kakimura, Kazuhisa Makino

Research output: Contribution to journalArticlepeer-review


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 the combined parameter. We also show that if we drop any of the three parameters, then the LCP is NP-hard or W[1]-hard. In addition, we show the nonexistence of a polynomial kernel for the LCP unless coNP ⊆ NP/poly.

Original languageEnglish
Pages (from-to)42-65
Number of pages24
Issue number1
Publication statusPublished - 2017 Sept 1
Externally publishedYes


  • Linear complementarity problem
  • Parameterized complexity
  • Sparsity

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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