Approximation algorithms for facility location problems

Facility location problems are among the most well-studied problems in optimization literature. The simplest variant is the uncapacitated facility location problem, which we denoted by the UFLP. In the UFLP, we are given a set of possible facility locations and a set of clients. The problem seeks to find a set of locations to build/open facilities such that the sum of the cost of building/opening the facilities and the cost of serving each client from exactly one open facility is minimized. This problem is NP−hard. Therefore, many heuristics for finding good approximate solutions were developed. In this thesis we design approximation algorithms for several variants of the UFLP.