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Preprint 26-2007

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

Approximating Connected Facility Location Problems via Random Facility Sampling and Core Detouring
Friedrich Eisenbrand, Fabrizio Grandoni, Thomas Rothvoß, and Guido Schäfer
not available
approximation algorithms, network design problems, connected facility location, single-sink rent-or-buy
We present a simple randomized algorithmic framework for connected facility location problems. The basic idea is as follows: We run a black-box approximation algorithm for the unconnected facility location problem, randomly sample the clients, and open the facilities serving sampled clients in the approximate solution. Via a novel analytical tool, which we term core detouring, we show that this approach significantly improves over the previously best known approximation ratios for several NP-hard network design problems. For example, we reduce the approximation ratio for the connected facility location problem from 8.55 to 4.00, and for the single-sink rent-or-buy problem from 3.55 to 2.92. We show that our connected facility location algorithms can be derandomized at the expense of a slightly worse approximation ratio. The versatility of our framework is demonstrated by devising improved approximation algorithms also for other related problems.
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