The linear complementarity problems with a few variables per constraint

Hanna Sumita, Naonori Kakimura, Kazuhisa Makino

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we consider the sparse linear complementarity problem, denoted by k-LCP: the coefficient matrices are restricted to have at most k nonzero entries per row. It is known that the 1-LCP is solvable in linear time, and the 3-LCP is strongly NP-hard. We show that the 2-LCP is strongly NP-hard, and it can be solved in polynomial time if it is sign-balanced, i.e., each row of the matrix has at most one positive and one negative entry. Our second result matches the currently best-known complexity bound for the corresponding sparse linear feasibility problem. In addition, we show that an integer variant of the sign-balanced 2-LCP is weakly NP-hard and pseudo-polynomially solvable, and the generalized 1-LCP is strongly NP-hard.

Original languageEnglish
Pages (from-to)1015-1026
Number of pages12
JournalMathematics of Operations Research
Volume40
Issue number4
DOIs
Publication statusPublished - 2015 Nov 1
Externally publishedYes

Fingerprint

Linear Complementarity Problem
NP-complete problem
Polynomials
Linear Time
Polynomial time
Integer
Linear complementarity problem
NP-hard
Coefficient

Keywords

  • Combinatorial algorithm
  • Linear complementarity problem
  • NP-hardness
  • Polynomial solvability
  • Two-variable constraints

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Cite this

The linear complementarity problems with a few variables per constraint. / Sumita, Hanna; Kakimura, Naonori; Makino, Kazuhisa.

In: Mathematics of Operations Research, Vol. 40, No. 4, 01.11.2015, p. 1015-1026.

Research output: Contribution to journalArticle

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