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Fast Algorithms for max independent set

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Abstract

We first propose a method, called “bottom-up method” that, informally, “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and we show an easy though non-trivial application of it to the min set cover problem. We then tackle max independent set. Here, we propagate improvements of worst-case complexity from graphs of average degree d to graphs of average degree greater than d. Indeed, using algorithms for max independent set in graphs of average degree 3, we successively solve max independent set in graphs of average degree 4, 5 and 6. Then, we combine the bottom-up technique with measure and conquer techniques to get improved running times for graphs of maximum degree 5 and 6 but also for general graphs. The computation bounds obtained for max independent set are O ∗(1.1571n), O ∗(1.1895n) and O ∗(1.2050n), for graphs of maximum (or more generally average) degree 4, 5 and 6 respectively, and O ∗(1.2114n) for general graphs. These results improve upon the best known results for these cases for polynomial space algorithms.

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Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cédex 16, France

    Nicolas Bourgeois, Bruno Escoffier & Vangelis T. Paschos

  2. Department of Information and Computing Sciences, Universiteit Utrecht, Utrecht, The Netherlands

    Johan M. M. van Rooij

Authors
  1. Nicolas Bourgeois
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  2. Bruno Escoffier
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  3. Vangelis T. Paschos
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  4. Johan M. M. van Rooij
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Corresponding author

Correspondence to Bruno Escoffier.

Additional information

Research supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010. Parts of this paper have been presented at SWAT’10, LNCS 6139 and at TAMC’10, LNCS 6108.

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Bourgeois, N., Escoffier, B., Paschos, V.T. et al. Fast Algorithms for max independent set . Algorithmica 62, 382–415 (2012). https://doi.org/10.1007/s00453-010-9460-7

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  • DOI: https://doi.org/10.1007/s00453-010-9460-7

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