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FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

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Abstract

Finding large (and generally maximal) independent sets of vertices in a given graph is a fundamental problem in distributed computing. Applications include, for example, facility location and backbone formation in wireless ad hoc networks. In this paper, we study a decentralized (or distributed) algorithm inspired by the calling behavior of male Japanese tree frogs, originally introduced for the graph-coloring problem, for its potential usefulness in the context of finding large independent sets. Moreover, we adapt this algorithm to directly produce maximal independent sets without the necessity of first producing a graph-coloring solution. Both algorithms are compared to a wide range of decentralized algorithms from the literature on a diverse set of benchmark instances for the maximal independent set problem. The results show that both algorithms compare very favorably to their competitors.

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Notes

  1. Note that, for simplicity and without loss of generality, natural numbers greater than zero are used to uniquely identify colors.

  2. Note that Eq. (2) is strongly inspired by a model of Japanese tree frogs’ desynchronization behavior from Aihara et al. (2008). We refer the readers interested in the biological background of the FrogCOL algorithm to Hernández and Blum (2012).

  3. Note that although in these graphs the nodes have spatial coordinates, these have not been used to plot the graph. Indeed, all the graphs in the figure have been created using the ‘neato’ layout of the dot software.

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Acknowledgments

This work was supported by Projects TIN2012-37930, TIN2013-41272P and TIN2007-66523 of the Spanish Government, and Project 2009-SGR1137 of the Generalitat de Catalunya. In addition, support is acknowledged from IKERBASQUE (Basque Foundation for Science) and the Basque Saiotek and Research Groups 2013-2018 (IT-609-13) programs. Our experiments have been executed in the High Performance Computing Environment managed by RDlab (http://rdlab.lsi.upc.edu), and we would like to thank them for their support.

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Authors and Affiliations

  1. University of the Basque Country UPV/EHU, San Sebastian, Spain

    Christian Blum & Borja Calvo

  2. Ikerbasque, Basque Foundation for Science, Bilbao, Spain

    Christian Blum

  3. ALBCOM Research Group, Universitat Politécnica de Catalunya, Barcelona, Spain

    Maria J. Blesa

Authors
  1. Christian Blum
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  2. Borja Calvo
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  3. Maria J. Blesa
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Correspondence to Christian Blum.

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Blum, C., Calvo, B. & Blesa, M.J. FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs. Swarm Intell 9, 205–227 (2015). https://doi.org/10.1007/s11721-015-0110-1

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