Georgia Institute of Technology College of Sciences

Local search is one of the oldest known optimization techniques. It has been studied extensively by Newton, Euler, etc. It is known that this technique gives the optimum solution if the function being optimized is concave(maximization) or convex (minimization). However, in the general case it may only produce a "locally optimum" solution. We study how to use this technique for a class of facility location problems and give the currently best known approximation guarantees for the problem and a matching "locality gap".