This paper deals with the issue of allocating and utilizing centers in a distributed network, in its various forms. The paper discusses the significant parameters of center allocation, defines the resulting optimization problems, and proposes several approximation algorithms for selecting centers and for distributing the users among them. We concentrate mainly on balanced versions of the problem, i.e., in which it is required that the assignment of clients to centers be as balanced as possible. The main results are constant ratio approximation algorithms for the balanced -centers and balanced -weighted centers problems, and logarithmic ratio approximation algorithms for the ae-dominating set and the k-tolerant set problems. School of Library and Information, The Hebrew University, Jerusalem 9xxxx, Israel. This work was carried out while the author was with the Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science. y Department of Applied M...

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation algorithms for two different versions of this problem that achieve approximation factors of 5 and 6. We also study some generalizations of this problem. 1. Introduction The basic K-center problem is a fundamental facility location problem [17] and is defined as follows: given an edge-weighted graph G = (V; E) find a subset S ` V of size at most K such that each vertex in V is "close" to some vertex in S. More formally, the objective function is defined as follows: min S`V max u2V min v2S d(u; v) where d is the distance function. For example, one may wish to install K fire stations and mi...

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Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links changes with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the K-center problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good time-invariant solutions. 1. Introduction Previous theoretical work on fac...