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A Best Possible Heuristic for the k-Center Problem
Abstract
In this paper we present a 2-approximation algorithm for the k-center problem with triangle inequality. This result is “best possible” since for any δ < 2 the existence of δ-approximation algorithm would imply that P = NP. It should be noted that no δ-approximation algorithm, for any constant δ, has been reported to date. Linear programming duality theory provides interesting insight to the problem and enables us to derive, in O(|E| log |E|) time, a solution with value no more than twice the k-center optimal value. A by-product of the analysis is an O(|E|) algorithm that identifies a dominating set in G 2, the square of a graph G, the size of which is no larger than the size of the minimum dominating set in the graph G. The key combinatorial object used is called a strong stable set, and we prove the NP-completeness of the corresponding decision problem.
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Metadata
- Authors
- Hochbaum, D. S., & Shmoys, D. B.
- Venue
- Mathematics of Operations Research
- Published
- 1985-05
- Volume
- 10
- Issue
- 2
- Pages
- 180-184
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2073583237
- Cited by
- 921
- References
- 0
- FWCI
- 4.44
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hochbaum, D. S., & Shmoys, D. B. (1985). A Best Possible Heuristic for the k-Center Problem. Mathematics of Operations Research. https://doi.org/10.1287/moor.10.2.180
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