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This paper is divided into two parts. In the first part of this paper, we present a 2-approximation algorithm for the soft-capacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algorithm for the linear facility location problem, and a… (More)

We consider the problem of computing the outer-radii of point sets. In this problem, we are given integers n, d, k where k ≤ d, and a set P of n points in R d. The goal is to compute the outer k-radius of P , denoted by R k (P), which is the minimum, over all (d−k)-dimensional flats F , of max p∈P d(p, F), where d(p, F) is the Euclidean distance between the… (More)

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