Abstract
The facility location problem consists of a set of facilities \(\mathcal{F}\), a set of clients \(\mathcal{C}\), an opening cost f i associated with each facility x i , and a connection cost D(x i ,y j ) between each facility x i and client y j . The goal is to find a subset of facilities to open, and to connect each client to an open facility, so as to minimize the total facility opening costs plus connection costs. This paper presents the first expected-sub-logarithmic-round distributed O(1)-approximation algorithm in the \(\mathcal{CONGEST}\) model for the metric facility location problem on the complete bipartite network with parts \(\mathcal{F}\) and \(\mathcal{C}\). Our algorithm has an expected running time of O((loglogn)3) rounds, where \(n = |\mathcal{F}| + |\mathcal{C}|\). This result can be viewed as a continuation of our recent work (ICALP 2012) in which we presented the first sub-logarithmic-round distributed O(1)-approximation algorithm for metric facility location on a clique network. The bipartite setting presents several new challenges not present in the problem on a clique network. We present two new techniques to overcome these challenges.
This work is supported in part by National Science Foundation grant CCF 0915543.
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Hegeman, J., Pemmaraju, S.V. (2013). A Super-Fast Distributed Algorithm for Bipartite Metric Facility Location. In: Afek, Y. (eds) Distributed Computing. DISC 2013. Lecture Notes in Computer Science, vol 8205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41527-2_36
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