Approximating the k-Set Packing problem by local improvements

Martin Fürer, Huiwen Yu

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

    9 Citations (Scopus)

    Abstract

    We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

    Original languageEnglish (US)
    Title of host publicationCombinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers
    PublisherSpringer Verlag
    Pages408-420
    Number of pages13
    ISBN (Print)9783319091730
    DOIs
    StatePublished - Jan 1 2014
    Event3rd International Symposium on Combinatorial Optimization, ISCO 2014 - Lisbon, Portugal
    Duration: Mar 5 2014Mar 7 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8596 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other3rd International Symposium on Combinatorial Optimization, ISCO 2014
    CountryPortugal
    CityLisbon
    Period3/5/143/7/14

    Fingerprint

    Set Packing
    Packing Problem
    Approximation
    Local Algorithms
    Exponential time
    Locality
    Polynomial-time Algorithm
    Polynomials

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Fürer, M., & Yu, H. (2014). Approximating the k-Set Packing problem by local improvements. In Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers (pp. 408-420). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8596 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-09174-7_35
    Fürer, Martin ; Yu, Huiwen. / Approximating the k-Set Packing problem by local improvements. Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag, 2014. pp. 408-420 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    Fürer, M & Yu, H 2014, Approximating the k-Set Packing problem by local improvements. in Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8596 LNCS, Springer Verlag, pp. 408-420, 3rd International Symposium on Combinatorial Optimization, ISCO 2014, Lisbon, Portugal, 3/5/14. https://doi.org/10.1007/978-3-319-09174-7_35

    Approximating the k-Set Packing problem by local improvements. / Fürer, Martin; Yu, Huiwen.

    Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag, 2014. p. 408-420 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8596 LNCS).

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

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    AB - We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

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    Fürer M, Yu H. Approximating the k-Set Packing problem by local improvements. In Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers. Springer Verlag. 2014. p. 408-420. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-09174-7_35