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Fast Distributed Algorithms for LP-Type Problems of Low Dimension

Authors Kristian Hinnenthal, Christian Scheideler, Martijn Struijs

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Author Details

Kristian Hinnenthal
  • Paderborn University, Germany
Christian Scheideler
  • Paderborn University, Germany
Martijn Struijs
  • TU Eindhoven, The Netherlands

Funding

K. Hinnenthal and C. Scheideler are supported by the DFG SFB 901 (On-The-Fly Computing).

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Kristian Hinnenthal, Christian Scheideler, and Martijn Struijs. Fast Distributed Algorithms for LP-Type Problems of Low Dimension. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.DISC.2019.23

Abstract

In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest enclosing ball and polytope distance, and set problems like hitting set and set cover. In the gossip model, a node can only push information to or pull information from nodes chosen uniformly at random. Protocols for the gossip model are usually very practical due to their fast convergence, their simplicity, and their stability under stress and disruptions. Our algorithms are very efficient (logarithmic rounds or better with just polylogarithmic communication work per node per round) whenever the combinatorial dimension of the given LP-type problem is constant, even if the size of the given LP-type problem is polynomially large in the number of nodes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Mathematical optimization
Keywords
  • LP-type problems
  • linear optimization
  • distributed algorithms
  • gossip algorithms

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