Approximating the Online Set Multicover Problems via Randomized Winnowing View Full Text


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Chapter Info

DATE

2005

AUTHORS

Piotr Berman , Bhaskar DasGupta

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{S}$\end{document} of subsets of V with a positive real cost for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S \in \mathcal{S}$\end{document}, and a “coverage factor” (positive integer) k. A subset {i0, i1,...} ⊆ V of elements are presented online in an arbitrary order. When each element ip is presented, we are also told the collection of all (at least k) sets \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{S}_{i_p} \subseteq \mathcal{S}$\end{document} and their costs in which ip belongs and we need to select additional sets from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{S}_{i_p}$\end{document} if necessary such that our collection of selected sets contains at leastk sets that contain the element ip. The goal is to minimize the total cost of the selected sets. 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]. More... »

PAGES

110-121

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/11534273_11

DOI

http://dx.doi.org/10.1007/11534273_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021364545


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