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Sparse Linear Complementarity Problems

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Algorithms and Complexity (CIAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7878))

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Abstract

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(n 3 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.

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Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, University of Tokyo, Tokyo, 113-8656, Japan

    Hanna Sumita & Kazuhisa Makino

  2. College of Arts and Sciences, University of Tokyo, Tokyo, 153-8902, Japan

    Naonori Kakimura

Authors
  1. Hanna Sumita
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  2. Naonori Kakimura
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  3. Kazuhisa Makino
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Editor information

Editors and Affiliations

  1. School of Engineering, Department of Computer Engineering and Informatics, University of Patras, 265 00, Patras, Greece

    Paul G. Spirakis

  2. LSI Department, Edif Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Maria Serna

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Sumita, H., Kakimura, N., Makino, K. (2013). Sparse Linear Complementarity Problems. In: Spirakis, P.G., Serna, M. (eds) Algorithms and Complexity. CIAC 2013. Lecture Notes in Computer Science, vol 7878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38233-8_30

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  • DOI: https://doi.org/10.1007/978-3-642-38233-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38232-1

  • Online ISBN: 978-3-642-38233-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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