Simultaneous source location

Authors:
Konstantin Andreev;Charles Garrod;Daniel Golovin;Bruce Maggs;Adam Meyerson
Affiliations:
Chatham Financial, Kennett Square, PA;Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA and Akamai Technologies;UCLA, Los Angeles, CA
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2009

Citing 18
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Abstract

We consider the problem of simultaneous source location: selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an O(log D)-approximation algorithm, where D is the sum of demands, and prove matching Ω(log D) hardness results assuming P ≠ NP. For undirected trees, we give an exact algorithm and show how this can be combined with a result of Räcke to give a solution that exceeds edge capacities by at most O(log2 n log log n), where n is the number of nodes. For undirected graphs of bounded treewidth we show that the problem is still NP-hard, but we are able to give a PTAS with at most (1 + &epsis;) violation of the capacities for arbitrarily small &epsis;, or a (k+1) approximation with exact capacities, where k is the treewidth.