We present improved combinatorial approximation algorithms for the uncapacitated facility location problem. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2.414+ in Õ(n/ ) time. This also yields a bicriteria approximation tradeoff of (1 + γ, 1 + 2/γ) for facility cost ve...

We address optimal group manipulation in multidimensional, multi-facility location problems. We focus on two families of mechanisms, generalized median and quantile mechanisms, evaluating the difficulty of group manipulation of these mechanisms. We show that, in the case of single-facility problems, optimal group manipulation can be formulated as a linear or second-order cone program, under the...

A general approach to optimally solve multiple facility location problems based on the “Big Triangle Small Triangle” approach to solving single facility problems is proposed. The proposed procedure is especially effective when the solution is constrained to a given polygon such as the convex hull of demand points. The procedure is tested on the two facilities Weber problem with attraction and r...

We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do not need any bound based on the solution to the dual LP program. Besides obtaining the optimal bifactor approximation as do Byrka and Aardal, we can now also s...

This paper surveys approximation algorithms for various facility location problems, mostly with detailed proofs. It resulted from lecture notes of a course held at the University of Bonn in the winter term 2004/2005.

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We present new approximation algorithms for several facility location problems. In each facility location problem that we study, there is a set of locations at which we may build a facility (such as a warehouse), where the cost of building at location i is fi; furthermore, there is a set of client locations (such as stores) that require to be serviced by a facility, and if a client at location ...

The bounded k-median problem is to select in an undirected graph G = (V, E) a set S of k vertices such that the distance from any vertex v ∈ V to S is at most a given bound d and the average distance from vertices V\S to S is minimized. We present randomized algorithms for several versions of this problem and we prove some inapproximability results. We also study the bounded version of the unca...

High performance computing applied to competitive facility location and design problems: single and multi-objective optimization algorithms A mis padres, a mi hermano y a Manu Agradecimientos En primer lugar me gustaría agradecer a mis tres supervisores, Dra. D Prefacio La localización de servicios pretende encontrar el emplazamiento de uno o más centros Esta tesis, " High performance computing...