Local search heuristics for k-Median and facility location problems

Arya, Vijay ; Garg, Naveen ; Khandekar, Rohit ; Meyerson, Adam ; Munagala, Kamesh ; Pandit, Vinayaka (2004) Local search heuristics for k-Median and facility location problems SIAM Journal on Computing, 33 (3). pp. 544-562. ISSN 0097-5397

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Official URL: http://epubs.siam.org/doi/abs/10.1137/S00975397024...

Related URL: http://dx.doi.org/10.1137/S0097539702416402


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 a local search for k-median that provides a bounded performance guarantee with only k medians. This also improves the previous known 4 approximation for this problem. For uncapacitated facility location, we show that local search, which permits adding, dropping, and swapping a facility, has a locality gap of 3. This improves the bound of 5 given by M. Korupolu, C. Plaxton and R. Rajaraman [Analysis of a Local Search Heuristic for Facility Location Problems, Technical Report 98-30, DIMACS, 1998]. We also consider a capacitated facility location problem where each facility has a capacity and we are allowed to open multiple copies of a facility. For this problem we introduce a new local search operation which opens one or more copies of a facility and drops zero or more facilities. We prove that this local search has a locality gap between 3 and 4.

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