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 language | English (US) |
|---|---|
| Pages (from-to) | 110-121 |
| Number of pages | 12 |
| Journal | Lecture Notes in Computer Science |
| Volume | 3608 |
| State | Published - Oct 24 2005 |
| Event | 9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada Duration: Aug 15 2005 → Aug 17 2005 |
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All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
Cite this
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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 journal › Conference article
TY - JOUR
T1 - Approximating the online set multicover problems via randomized winnowing
AU - Berman, Piotr
AU - DasGupta, Bhaskar
PY - 2005/10/24
Y1 - 2005/10/24
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].
AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=26844438073&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:26844438073
VL - 3608
SP - 110
EP - 121
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
ER -