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