Packing-based approximation algorithm for the k-set cover problem

Martin Furer, Huiwen Yu

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Citation (Scopus)

    Abstract

    We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k ≥ 7, Restricted k-Set Packing for k = 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of H k - 0.6402 + Θ(1/k), where H k is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
    Pages484-493
    Number of pages10
    DOIs
    StatePublished - Dec 26 2011
    Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
    Duration: Dec 5 2011Dec 8 2011

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume7074 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other22nd International Symposium on Algorithms and Computation, ISAAC 2011
    CountryJapan
    CityYokohama
    Period12/5/1112/8/11

    Fingerprint

    Set Packing
    Set Cover
    Approximation algorithms
    Packing
    Approximation Algorithms
    Heuristics
    Harmonic number
    Combinatorial argument
    Approximation
    Best Approximation
    Local Search

    All Science Journal Classification (ASJC) codes

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Furer, M., & Yu, H. (2011). Packing-based approximation algorithm for the k-set cover problem. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings (pp. 484-493). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_50
    Furer, Martin ; Yu, Huiwen. / Packing-based approximation algorithm for the k-set cover problem. Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. 2011. pp. 484-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    abstract = "We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k ≥ 7, Restricted k-Set Packing for k = 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of H k - 0.6402 + Θ(1/k), where H k is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.",
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    Furer, M & Yu, H 2011, Packing-based approximation algorithm for the k-set cover problem. in Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7074 LNCS, pp. 484-493, 22nd International Symposium on Algorithms and Computation, ISAAC 2011, Yokohama, Japan, 12/5/11. https://doi.org/10.1007/978-3-642-25591-5_50

    Packing-based approximation algorithm for the k-set cover problem. / Furer, Martin; Yu, Huiwen.

    Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. 2011. p. 484-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    AB - We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k ≥ 7, Restricted k-Set Packing for k = 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of H k - 0.6402 + Θ(1/k), where H k is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.

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    Furer M, Yu H. Packing-based approximation algorithm for the k-set cover problem. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. 2011. p. 484-493. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25591-5_50