Abstract
Solving an open problem of Jain and Vazirani [FOCS’99], we present Õ(n+m) time constant factor approximation algorithms for the k-median, k-center, and facility location problems with assignment costs being shortest path distances in a weighted undirected graph with n nodes and m edges.
For all of these location problems, Õ(n 2) algorithms were already known, but here we are addressing large sparse graphs. An application could be placement of content distributing servers on the Internet. The Internet is large and changes so frequently that an Õ(n 2) time solution would likely be outdated long before completion.
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Thorup, M. (2001). Quick k-Median, k-Center, and Facility Location for Sparse Graphs. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_21
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DOI: https://doi.org/10.1007/3-540-48224-5_21
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