## Approximating connected facility location problems via Random facility sampling and core detouring

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.

Published in:
Proceeding of Nineteenth annual ACM-SIAM Symposium (SODA '08), 1174-1183
Presented at:
ACM-SIAM Symposium on Discrete Algorithms (SODA '08), San Francisco, California, 20-22.01.2008
Year:
2008
Laboratories: