Approximating the online set multicover problems via randomized winnowing

Piotr Berman, Bhaskar DasGupta

    Research output: Contribution to journalConference article

    1 Citation (Scopus)

    Abstract

    In this paper, we consider the weighted online set k-multicover problem. In this problem, we have an universe V of elements, a family S of subsets of V with a positive real cost for every S G ε S, and a "coverage factor" (positive integer) k. A subset {i o, i 1...} ⊆ V of elements are presented online in an arbitrary order. When each element i p is presented, we are also told the collection of all (at least k) sets S ip ⊆ S and their costs in which p belongs and we need to select additional sets from S ip if necessary such that our collection of selected sets contains at least k sets that contain the element i p. The goal is to minimize the total cost of the selected sets 1. In this paper, we describe a new randomized algorithm for the online multicover problem based on the randomized winnowing approach of [11]. This algorithm generalizes and improves some earlier results in [1]. We also discuss lower bounds on competitive ratios for deterministic algorithms for general k based on the approaches in [1].

    Original languageEnglish (US)
    Pages (from-to)110-121
    Number of pages12
    JournalLecture Notes in Computer Science
    Volume3608
    StatePublished - Oct 24 2005
    Event9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada
    Duration: Aug 15 2005Aug 17 2005

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    Costs
    Subset
    Competitive Ratio
    Deterministic Algorithm
    Randomized Algorithms
    Coverage
    Lower bound
    Minimise
    Generalise
    Integer
    Necessary
    Arbitrary
    Family

    All Science Journal Classification (ASJC) codes

    • Computer Science (miscellaneous)

    Cite this

    Berman, Piotr ; DasGupta, Bhaskar. / Approximating the online set multicover problems via randomized winnowing. In: Lecture Notes in Computer Science. 2005 ; Vol. 3608. pp. 110-121.
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    Approximating the online set multicover problems via randomized winnowing. / Berman, Piotr; DasGupta, Bhaskar.

    In: Lecture Notes in Computer Science, Vol. 3608, 24.10.2005, p. 110-121.

    Research output: Contribution to journalConference article

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    AU - DasGupta, Bhaskar

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    N2 - In this paper, we consider the weighted online set k-multicover problem. In this problem, we have an universe V of elements, a family S of subsets of V with a positive real cost for every S G ε S, and a "coverage factor" (positive integer) k. A subset {i o, i 1...} ⊆ V of elements are presented online in an arbitrary order. When each element i p is presented, we are also told the collection of all (at least k) sets S ip ⊆ S and their costs in which p belongs and we need to select additional sets from S ip if necessary such that our collection of selected sets contains at least k sets that contain the element i p. The goal is to minimize the total cost of the selected sets 1. In this paper, we describe a new randomized algorithm for the online multicover problem based on the randomized winnowing approach of [11]. This algorithm generalizes and improves some earlier results in [1]. We also discuss lower bounds on competitive ratios for deterministic algorithms for general k based on the approaches in [1].

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