Complexity of single-swap heuristics for metric facility location and related problems

Abstract

Metric facility location and K -means are well-known prob-lems of combinatorial optimization. Both admit a fairly simple heuris-tic called single-swap, which adds, drops or swaps open facilities until it reaches a local optimum. For both problems, it is known that this algorithm produces a solution that is at most a constant factor worse than the respective global optimum. In this paper, we show that single-swap applied to the weighted metric uncapacitated facility location and weighted discrete K -means problem is tightly PLS-complete and hence has exponential worst-case running time.