Exact and approximation algorithms for geometric and capacitated set cover problems

Piotr Berman, Marek Karpinski, Andrzej Lingas

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

    3 Scopus citations

    Abstract

    First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general (non-necessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets. We show that any polynomial-time algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r+1.357. The composition of these two results yields a polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357.

    Original languageEnglish (US)
    Title of host publicationComputing and Combinatorics - 16th Annual International Conference, COCOON 2010, Proceedings
    Pages226-234
    Number of pages9
    DOIs
    Publication statusPublished - Aug 3 2010
    Event16th Annual International Computing and Combinatorics Conference, COCOON 2010 - Nha Trang, Viet Nam
    Duration: Jul 19 2010Jul 21 2010

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume6196 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other16th Annual International Computing and Combinatorics Conference, COCOON 2010
    CountryViet Nam
    CityNha Trang
    Period7/19/107/21/10

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    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, P., Karpinski, M., & Lingas, A. (2010). Exact and approximation algorithms for geometric and capacitated set cover problems. In Computing and Combinatorics - 16th Annual International Conference, COCOON 2010, Proceedings (pp. 226-234). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6196 LNCS). https://doi.org/10.1007/978-3-642-14031-0_26