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Large-Scale Distributed Algorithms for Facility Location with Outliers

Authors Tanmay Inamdar, Shreyas Pai, Sriram V. Pemmaraju

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Tanmay Inamdar
  • Department of Computer Science, The University of Iowa, Iowa, USA
Shreyas Pai
  • Department of Computer Science, The University of Iowa, Iowa, USA
Sriram V. Pemmaraju
  • Department of Computer Science, The University of Iowa, Iowa, USA

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Tanmay Inamdar, Shreyas Pai, and Sriram V. Pemmaraju. Large-Scale Distributed Algorithms for Facility Location with Outliers. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.OPODIS.2018.5

Abstract

This paper presents fast, distributed, O(1)-approximation algorithms for metric facility location problems with outliers in the Congested Clique model, Massively Parallel Computation (MPC) model, and in the k-machine model. The paper considers Robust Facility Location and Facility Location with Penalties, two versions of the facility location problem with outliers proposed by Charikar et al. (SODA 2001). The paper also considers two alternatives for specifying the input: the input metric can be provided explicitly (as an n x n matrix distributed among the machines) or implicitly as the shortest path metric of a given edge-weighted graph. The results in the paper are: - Implicit metric: For both problems, O(1)-approximation algorithms running in O(poly(log n)) rounds in the Congested Clique and the MPC model and O(1)-approximation algorithms running in O~(n/k) rounds in the k-machine model. - Explicit metric: For both problems, O(1)-approximation algorithms running in O(log log log n) rounds in the Congested Clique and the MPC model and O(1)-approximation algorithms running in O~(n/k) rounds in the k-machine model. Our main contribution is to show the existence of Mettu-Plaxton-style O(1)-approximation algorithms for both Facility Location with outlier problems. As shown in our previous work (Berns et al., ICALP 2012, Bandyapadhyay et al., ICDCN 2018) Mettu-Plaxton style algorithms are more easily amenable to being implemented efficiently in distributed and large-scale models of computation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Distributed algorithms
  • Theory of computation → MapReduce algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Distributed Algorithms
  • Clustering with Outliers
  • Metric Facility Location
  • Massively Parallel Computation
  • k-machine model
  • Congested Clique

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