AnO(log*n) Approximation Algorithm for the Asymmetricp-Center Problem

doi:10.1006/jagm.1997.0921

Journal of Algorithms

Volume 27, Issue 2, May 1998, Pages 259-268

https://doi.org/10.1006/jagm.1997.0921 Get rights and content

Abstract

The input to the asymmetricp-center problem consists of an integerpand ann × ndistance matrixDdefined on a vertex setVof sizen, whered_ijgives the distance fromitoj. The distances are assumed to obey the triangle inequality. For a subsetS ⊆ Vthe radius ofSis the minimum distanceRsuch that every point inVis at a distance at mostRfrom some point inS. Thep-center problem consists of picking a setS ⊆ Vof sizepto minimize the radius. This problem is known to be NP-complete.

For the symmetric case, whend_ij = d_ji, approximation algorithms that deliver a solution to within 2 of the optimal are known. David Shmoys, in his article [11], mentions that nothing was known about the asymmetric case. We present an algorithm that achieves a ratio ofO(log*n).

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There are more references available in the full text version of this article.

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^☆: W. CookL. LovaszP. Seymour

^*: E-mail:[email protected].

^†: E-mail:[email protected].

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Regular ArticleAnO(log*n) Approximation Algorithm for the Asymmetricp-Center Problem☆

Abstract

Discrete Math.

The Design and Analysis of Computer Algorithms

Combinatorics

A greedy heuristic for the set covering problem

Math. Oper. Res.

A simple heuristic for thep

Oper. Res. Lett.

Computers and Intractability: A Guide to the Theory of NP-Completeness

Regular Article
AnO(log*n) Approximation Algorithm for the Asymmetricp-Center Problem☆