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The max quasi-independent set problem

Author

Listed:
  • N. Bourgeois

    (CNRS FRE 3234 and Université Paris-Dauphine)

  • A. Giannakos

    (CNRS FRE 3234 and Université Paris-Dauphine)

  • G. Lucarelli

    (CNRS FRE 3234 and Université Paris-Dauphine
    Athens University of Economics and Business)

  • I. Milis

    (Athens University of Economics and Business)

  • V. T. Paschos

    (CNRS FRE 3234 and Université Paris-Dauphine)

  • O. Pottié

    (CNRS FRE 3234 and Université Paris-Dauphine)

Abstract

In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, f-max quasi-independent set, consists of, given a graph and a non-decreasing function f, finding a maximum size subset Q of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to f(|Q|). For this problem, we show an exact solution method that runs within time $O^{*}(2^{\frac{d-27/23}{d+1}n})$ on graphs of average degree bounded by d. For the most specifically defined γ-max quasi-independent set and k-max quasi-independent set problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.

Suggested Citation

  • N. Bourgeois & A. Giannakos & G. Lucarelli & I. Milis & V. T. Paschos & O. Pottié, 2012. "The max quasi-independent set problem," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 94-117, January.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:1:d:10.1007_s10878-010-9343-5
    DOI: 10.1007/s10878-010-9343-5
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    References listed on IDEAS

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    1. Leland H. Hartwell & John J. Hopfield & Stanislas Leibler & Andrew W. Murray, 1999. "From molecular to modular cell biology," Nature, Nature, vol. 402(6761), pages 47-52, December.
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    Cited by:

    1. Bourgeois, Nicolas & Giannakos, Aristotelis & Lucarelli, Giorgio & Milis, Ioannis & Paschos, Vangelis Th., 2017. "Exact and superpolynomial approximation algorithms for the densest k-subgraph problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 894-903.
    2. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.

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