An algorithm for finding a k-median in a directed tree

doi:10.1016/S0020-0190(00)00026-0

Information Processing Letters

Volume 74, Issues 1–2, April 2000, Pages 81-88

https://doi.org/10.1016/S0020-0190(00)00026-0 Get rights and content

Abstract

We consider the problem of finding a $k$ -median in a directed tree. We present an algorithm that computes a $k$ -median in $O (Pk^{2})$ time where $k$ is the number of resources to be placed and $P$ is the path length of the tree. In the case of a balanced tree, this implies $O (k^{2} n log n)$ time, in a random tree $O (k^{2} n^{3/2}),$ while in the worst case $O (k^{2} n^{2})$ . Our method employs dynamic programming and uses $O (nk)$ space, while the best known algorithms for undirected trees require $O (n^{2} k)$ space.

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¹: Most of this work was done while visiting the Hong Kong University of Science & Technology. Research partially supported by HK RGC CERG Grant HKUST652/95E.

²: Research supported in part by NSF CAREER Award grant ANI-9875513. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

³: Research partially supported by Italian Ministry of University and Scientific and Technological Research under the Project “Algorithms for Large Data Sets: Science and Engineering”. Most of this work was done while visiting the Hong Kong University of Science & Technology. URL: http://www.info.uniroma2.it/~italiano.

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An algorithm for finding a k-median in a directed tree

Abstract

Placing resources on a growing line

J. Algorithms

An algorithmic approach to network location problems. II: The p-medians

SIAM. J. Appl. Math.

An algorithm for finding a $k$ -median in a directed tree

An algorithmic approach to network location problems. II: The $p$ -medians