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 \(\mathcal{S}\) of subsets of V with a positive real cost for every \(S \in \mathcal{S}\), and a “coverage factor” (positive integer) k. A subset {i 0, 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 \(\mathcal{S}_{i_p} \subseteq \mathcal{S}\) and their costs in which i p belongs and we need to select additional sets from \(\mathcal{S}_{i_p}\) if necessary such that our collection of selected sets contains at leastk sets that contain the element i p . 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].
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Berman, P., DasGupta, B. (2005). Approximating the Online Set Multicover Problems via Randomized Winnowing. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_11
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DOI: https://doi.org/10.1007/11534273_11
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