On the approximation of the minimum disturbance p-facility location problem

Authors:
Giulia Galbiati
Affiliations:
Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Venue:
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Year:
2002

Citing 2
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Abstract

An n × m non-negative integer matrix D= {dij} is given, representing the disturbance that customer i receives by a facility at location j. We consider the problem of finding p facilities so that the maximum, over the n customers, of the sums of their disturbances is minimized. We show that this problem can be deterministically approximated within O(ρ(logn + log p)), where ρ is the ratio between the biggest and the smallest positive entry of D. We obtain this result by first taking a randomized rounding approach to the problem and then by derandomizing the algorithm by the method of conditional probabilities.