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The Maximum Matrix Contraction Problem

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Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem. Especially, we prove this problem to be NP-Complete and that every algorithm solving this problem is at most a \(2\sqrt{n}\)-approximation algorithm where n is the number of ones in the matrix. We then focus on efficient algorithms to solve the problem: an integer linear program and three heuristics.

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Notes

  1. 1.

    The meaning of \([\![p; q ]\!]\) is the list \([p,p+1,\dots , q]\).

  2. 2.

    The implementations can be found at https://github.com/mouton5000/MMCCode.

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Author information

Authors and Affiliations

  1. CEDRIC-CNAM, 292 Rue du Faubourg Saint Martin, 75003, Paris, France

    Dimitri Watel & Pierre-Louis Poirion

  2. ENSIIE, 1 Square de la Résistance, Evry, France

    Dimitri Watel

  3. ENSTA Paristech, Evry, France

    Pierre-Louis Poirion

Authors
  1. Dimitri Watel
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  2. Pierre-Louis Poirion
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Corresponding author

Correspondence to Dimitri Watel .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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© 2016 Springer International Publishing Switzerland

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Cite this paper

Watel, D., Poirion, PL. (2016). The Maximum Matrix Contraction Problem. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_37

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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