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Streaming Algorithms for Independent Sets in Sparse Hypergraphs

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Abstract

We give the first treatment of the classic independent set problem in graphs and hypergraphs in the streaming setting. The objective is to find space-efficient algorithms that output independent sets that are “combinatorially optimal”, that is, with size guarantee in terms of the degree sequence alone. Our main result is a randomized algorithm that achieves this using space in bits that is linear in the number of vertices. We use this to examine assumptions about the streaming model, and advocate the study of output-efficient algorithms that measure space usage relative to the size of the output solution. In that sense, our main algorithm uses space linear in the output size. We also examine algorithms that use little or no space in addition to the bits storing the output. Our algorithms fall also into an online streaming model, where output-changes can go only in one direction. In particular a feasible solution must be maintained at all times, and items that are removed from the solution can never reenter. We obtain tight bounds on deterministic algorithms for independent sets in graphs in that model.

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Acknowledgments

We thank Páll Melsted for helpful discussions.

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Authors and Affiliations

  1. ICE-TCS, School of Science and Engineering, Reykjavik University and deCODE genetics, 101, Reykjavík, Iceland

    Bjarni V. Halldórsson

  2. ICE-TCS, School of Computer Science, Reykjavik University, 101, Reykjavík, Iceland

    Magnús M. Halldórsson & Elena Losievskaja

  3. Department of Computer Science, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, USA

    Mario Szegedy

Authors
  1. Bjarni V. Halldórsson
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  2. Magnús M. Halldórsson
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  3. Elena Losievskaja
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  4. Mario Szegedy
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Corresponding author

Correspondence to Magnús M. Halldórsson.

Additional information

Magnús M. Halldórsson: Research supported by Grants 7000921,90032021 and 12003211 of the Icelandic Research Fund.

Mario Szegedy: Supported by NSF Grant EMT-0523866.

A preliminary version of this paper appeared in the Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP), Bordeaux, France, July 2010.

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Halldórsson, B.V., Halldórsson, M.M., Losievskaja, E. et al. Streaming Algorithms for Independent Sets in Sparse Hypergraphs. Algorithmica 76, 490–501 (2016). https://doi.org/10.1007/s00453-015-0051-5

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  • DOI: https://doi.org/10.1007/s00453-015-0051-5

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