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Local Search Heuristics for k-Median and Facility Location Problems
SIAM journal on computing (Print)
We analyze local search heuristics for the metric k-median and facility location problems. We define the locality gap of a local search procedure for a minimization problem as the maximum ratio of a locally optimum solution (obtained using this procedure) to the global optimum. For k-median, we show that local search with swaps has a locality gap of 5. Furthermore, if we permit up to p facilities to be swapped simultaneously, then the locality gap is 3 + 2/p. This is the first analysis of adoi:10.1137/s0097539702416402 fatcat:x3aew4w54jc4jexa6jf4bt65ga