Local search heuristics for k-median and facility location problems

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Arya, V; Garg, N; Khandekar, R; Meyerson, A; Munagala, K; Pandit, V

Published Date

  • July 28, 2004

Published In

Volume / Issue

  • 33 / 3

Start / End Page

  • 544 - 562

International Standard Serial Number (ISSN)

  • 0097-5397

Digital Object Identifier (DOI)

  • 10.1137/S0097539702416402

Citation Source

  • Scopus