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Super-Fast Distributed Algorithms for Metric Facility Location

  • Andrew Berns
  • James Hegeman
  • Sriram V. Pemmaraju
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

This paper presents a distributed O(1)-approximation algorithm in the \(\mathcal{CONGEST}\) model for the metric facility location problem on a size-n clique network that has an expected running time of O(loglogn ·log* n) rounds. Though metric facility location has been considered by a number of researchers in low-diameter settings, this is the first sub-logarithmic-round algorithm for the problem that yields an O(1)-approximation in the setting of non-uniform facility opening costs. Since the facility location problem is specified by Ω(n 2) bits of information, any fast solution in the \(\mathcal{CONGEST}\) model must be truly distributed. Our paper makes three main technical contributions. First, we show a new lower bound for metric facility location. Next, we demonstrate a reduction of the distributed metric facility location problem to the problem of computing an O(1)-ruling set of an appropriate spanning subgraph. Finally, we present a sub-logarithmic-round (in expectation) algorithm for computing a 2-ruling set in a spanning subgraph of a clique. Our algorithm accomplishes this by using a combination of randomized and deterministic sparsification.

Keywords

Facility Location Facility Location Problem Span Subgraph Unit Disk Graph Communication Round 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew Berns
    • 1
  • James Hegeman
    • 1
  • Sriram V. Pemmaraju
    • 1
  1. 1.Department of Computer ScienceThe University of IowaIowa CityUSA

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