Approximating the Online Set Multicover Problems Via Randomized Winnowing, to appear

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 ∈ 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 S ip ⊆ S and their costs in which i 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 o

Approximating the Online Set Multicover Problems Via Randomized Winnowing

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 ∈S, 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 Sip ⊆ S and their costs in which ip belongs and we need to select additional sets from Sip if necessary such that our collection of selected sets contains at least k sets that contain the element ip. The goal is to minimize the total cost of the selected sets 3. 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]

Approximating the Online Set Multicover Problems Via Randomized Winnowing

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 ∈ S, 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 Sip ⊆ S and their costs in which ip belongs and we need to select additional sets from Sip if necessary such that our collection of selected sets contains at least k sets that contain the element ip. The goal is to minimize the total cost of the selected sets1. In this paper, we describe a new randomized algorithm for the online multicover problem based on a randomized version of the winnowing approach of [14]. This algorithm generalizes and improves some earlier results in [1, 2]. We also discuss lower bounds on competitive ratios for deterministic algorithms for general k based on the approaches in [2]