Saurav Pandit
ABSTRACT
In this paper we present fast, distributed approximation algorithms for the metric facility location problem in the CONGEST model, where message sizes are bounded by O(log N) bits, N being the network size. We first show how to obtain a 7-approximation in O(log m + log n) rounds via the primal-dual method; here m is the number of facilities and n is the number of clients. Subsequently, we generalize this to a k-round algorithm, that for every constant k, yields an approximation factor of O(m2/√k ∙ n3/√k). These results answer a question posed by Moscibroda and Wattenhofer (PODC 2005). Our techniques are based on the primal-dual algorithm due to Jain and Vazirani (JACM 2001) and a rapid randomized sparsification of graphs due to Gfeller and Vicari (PODC 2007). These results complement the results of Moscibroda and Wattenhofer (PODC 2005) for non-metric facility location and extend the results of Gehweiler et al. (SPAA 2006) for uniform metric facility location.
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Index Terms
- Return of the primal-dual: distributed metric facilitylocation
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