Abstract
We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swap and prove that any locally optimum solution is no more than 3 times the global optimum. This improves on a result of Chudak and Williamson who proved an approximation ratio of \({3+2\sqrt{2}}\) for the same algorithm. We also provide an example which shows that any local search algorithm which uses only these three operations cannot achieve an approximation guarantee better than 3.
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