For a vertex v and a (k−1)-element subset P of vertices of a graph, one can define the distance from v to P in various ways, including the minimum, average, and maximum distance from v to P. Associated with each of these distances, one can define the keccentricity of the vertex v as the maximum distance over all P, and the k-eccentricity of the set P as the maximum distance over all v. If k = 2 one is back with the normal eccentricity. We study here the properties of these eccentricity measures, especially bounds on the associated radius (minimum k-eccentricity) and diameter (maximum k-eccentricity). 1

We consider a variant of the facility location problem with additional interference constraints of the form "not too many facilities can be close to a user". These constraints arise naturally in the placement of wireless access points or base stations. We model the interference in several (increasingly complex) ways, and show approximation algorithms for them. We also consider the assignment of frequencies to the facilities with the motivation that two facilities with dierent frequencies do not interfere. This leads to an interesting coloring variant of facility location. Our techniques show that interference constraints are not too hard to enforce in rounding schemes that preserve locality.

Abstract not found

Gonzalez’s algorithm Hochbaum-Shmoys ’ algorithm Plesnik’s algorithm