### 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) |
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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

*Lecture Notes in Computer Science*,

*3608*, 110-121.

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*Lecture Notes in Computer Science*, vol. 3608, pp. 110-121.

**Approximating the online set multicover problems via randomized winnowing.** / Berman, Piotr; DasGupta, Bhaskar.

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 -