We characterize inner product spaces in terms of the relationship between the relative Chebyshev center of a set and the absolute Cheby-shev center of an associated set. A consequence of the characterization is that an existing nite algorithm can be adapted to calculate the center of a nite set relative to a nite dimensional aane space. We also discuss the case where the constraint set is nonli...

We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...

In the k-median problem, given a set of locations, the goal is to select a subset of at most k centers so as to minimize the total cost of connecting each location to its nearest center. We study the uniform hard capacitated version of the k-median problem, in which each selected center can only serve a limited number of locations. Inspired by the algorithm of Charikar, Guha, Tardos and Shmoys,...

We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...

We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...

In the k-median problem, given a set of locations, the goal is to select a subset of at most k centers so as to minimize the total cost of connecting each location to its nearest center. We study the uniform hard capacitated version of the k-median problem, in which each selected center can only serve a limited number of locations. Inspired by the algorithm of Charikar, Guha, Tardos and Shmoys,...

In this work, we study a range of constrained versions the k-supplier and k-center problems. classical (unconstrained) problem, are given set clients C in metric space X, with distance function d(.,.). We also feasible facility locations L⊆X. The goal is to open F k facilities L minimize maximum any client closest facility, i.e., minimize, cost(F,C)≡maxj∈C⁡{d(F,j)}, where d(F,j) j F. problem sp...