Grandoni, Fabrizio and Gupta, Anupam and Leonardi, Stefano and Miettinen, Pauli and Sankowski, Piotr and Singh, Mohit
(2013)
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Set Covering with Our Eyes Closed.
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In: Foundations of Computer Science FOCS '08. IEEE 49th Annual IEEE Symposium, 25.10.2008-28.10.2008, Philadelphia, PA.

## Abstract

Given a universe U of n elements and a weighted collection l of m subsets of U, the universal set cover problem is to a-priori map each element u epsi U to a set S(u) epsi l containing u, so that X sube U is covered by S(X)=UuepsiXS(u). The aim is finding a mapping such that the cost of S(X) is as close as possible to the optimal set-cover cost for X. (Such problems are also called oblivious or a-priori optimization problems.) Unfortunately, for every universal mapping, the cost of S(X) can be Omega(radicn) times larger than optimal if the set X is adversarially chosen. In this paper we study the performance on average, when X is a set of randomly chosen elements from the universe: we show how to efficiently find a universal map whose expected cost is O(log mn) times the expected optimal cost. In fact, we give a slightly improved analysis and show that this is the best possible. We generalize these ideas to weighted set cover and show similar guarantees to (non-metric) facility location, where we have to balance the facility opening cost with the cost of connecting clients to the facilities. We show applications of our results to universal multi-cut and disc-covering problems, and show how all these universal mappings give us stochastic online algorithms with the same competitive factors.

Item Type: | Article in conference proceedings or Presentation at a conference (Paper) |
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Subjects: | Computer sciences |

Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sullâ€™intelligenza artificiale USI-SUPSI |

Depositing User: | Fabrizio Grandoni |

Date Deposited: | 14 Mar 2014 08:22 |

Last Modified: | 23 May 2016 14:22 |

URI: | http://repository.supsi.ch/id/eprint/4474 |

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