We present two improved algorithms for weighted discrete p-center problem for tree networks with n vertices. One of our proposed algorithms runs in O(n logn + p log n log(n/p)) time. For all values of p, our algorithm thus runs as fast as or faster than the most efficient O(n log n) time algorithm obtained by applying Cole’s speed-up technique [10] to the algorithm due to Megiddo and Tamir [20]...

In an earlier paper Hud91], two \alternative" p-Center problems, where the centers serving customers must be chosen so that exactly one node from each of p prespeciied disjoint pairs of nodes is selected, were shown to be NP-complete. This paper considers a generalized version of these problems, in which the nodes from which the p servers are to be selected are partitioned into k sets and the n...

We develop a simple and practical exact algorithm for the problem of locating p facilities and assigning clients to them within capacity restrictions in order to minimize the maximum distance between a client and the facility to which it is assigned (capacitated p-center). The algorithm iteratively sets a maximum distance value within which it tries to assign all clients, and thus solves bin-pa...

The perceptual moment of occurrence of a syllable, its P-center, has frequently been examined by instructing subjects to adjust a series of speech sounds until they sounded isochronous. The present two experiments examined the effect of changing the instructions. In addition to the overall isochrony instructions, we asked subjects to align pairs of syllables so that the syllable onsets, vowel o...

The p-center problem is one of choosing p facilities from a set of candidates to satisfy the demands of n clients in order to minimize the maximum cost between a client and the facility to which it is assigned. In this article, PBS, a population based meta-heuristic for the p-center problem, is described. PBS is a genetic algorithm based meta-heuristic that uses phenotype crossover and directed...

Locating facilities on anywhere on a network is known as the absolute p-center location problem and it is proven to be NP-hard problem. Most of the recent approaches solve largescale vertex p-center location problem in which facilities can be located only on the nodes of the network. However, rarely algorithms are developed to solve large-scale absolute p-center problem. Particle swarm optimiza...

We study a generalization of the p{Center Problem, which we call the {Neighbor p{Center Problem (p{Center ()). Given a complete edge{ weighted network, the goal is to minimize the maximum distance of a client to its nearest neighbors in the set of p centers. We show that in general nding a O(2 poly(jV j)){approximation for p{ Center () is NP{hard, where jV j denotes the number of nodes in the n...

We consider the k-center problem, in which the centers are constrained to lie on two axis-parallel lines. Given a set of n weighted points in the plane, which are sorted according to their x-coordinates, we show how to test in O(n logn) time if k piercing points placed on two lines, parallel to the x-axis, can pierce all the disks of different radii centered at the n given points. This leads to...