An efficient distributed algorithm for constructing small dominating sets

L. Jia, R. Rajaraman, T. Suel

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

    Abstract

    The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O(log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual ACM Symposium on Principles of Distributed Computing
    Pages33-42
    Number of pages10
    StatePublished - 2001
    Event20th Annual ACM Symposium on Principles of Distributed Computing - Newport, Rhode Island, United States
    Duration: Aug 26 2001Aug 29 2001

    Other

    Other20th Annual ACM Symposium on Principles of Distributed Computing
    CountryUnited States
    CityNewport, Rhode Island
    Period8/26/018/29/01

    Fingerprint

    Parallel algorithms

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Hardware and Architecture

    Cite this

    Jia, L., Rajaraman, R., & Suel, T. (2001). An efficient distributed algorithm for constructing small dominating sets. In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing (pp. 33-42)

    An efficient distributed algorithm for constructing small dominating sets. / Jia, L.; Rajaraman, R.; Suel, T.

    Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. 2001. p. 33-42.

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

    Jia, L, Rajaraman, R & Suel, T 2001, An efficient distributed algorithm for constructing small dominating sets. in Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. pp. 33-42, 20th Annual ACM Symposium on Principles of Distributed Computing, Newport, Rhode Island, United States, 8/26/01.
    Jia L, Rajaraman R, Suel T. An efficient distributed algorithm for constructing small dominating sets. In Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. 2001. p. 33-42
    Jia, L. ; Rajaraman, R. ; Suel, T. / An efficient distributed algorithm for constructing small dominating sets. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing. 2001. pp. 33-42
    @inproceedings{faab525a7b184609b1bf94f22d64629e,
    title = "An efficient distributed algorithm for constructing small dominating sets",
    abstract = "The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O(log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.",
    author = "L. Jia and R. Rajaraman and T. Suel",
    year = "2001",
    language = "English (US)",
    pages = "33--42",
    booktitle = "Proceedings of the Annual ACM Symposium on Principles of Distributed Computing",

    }

    TY - GEN

    T1 - An efficient distributed algorithm for constructing small dominating sets

    AU - Jia, L.

    AU - Rajaraman, R.

    AU - Suel, T.

    PY - 2001

    Y1 - 2001

    N2 - The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O(log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.

    AB - The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NP-complete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the well-known logarithmic approximation result for the closely related set cover problem. We describe and analyze new randomized distributed algorithms for the dominating set problem that run in polylogarithmic time, independent of the diameter of the network, and that return a dominating set of size within a logarithmic factor from optimal, with high probability. In particular, our best algorithm runs in O(log n log Δ) rounds with high probability, where n is the number of nodes, Δ is one plus the maximum degree of any node, and each round involves a constant number of message exchanges among any two neighbors; the size of the dominating set obtained is within O(log Δ) of the optimal in expectation and within O(log n) of the optimal with high probability. We also describe generalizations to the weighted case and the case of multiple covering requirements.

    UR - http://www.scopus.com/inward/record.url?scp=0034782303&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0034782303&partnerID=8YFLogxK

    M3 - Conference contribution

    SP - 33

    EP - 42

    BT - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

    ER -