On the distributed complexity of the semi-matching problem

Andrzej Czygrinow, Michał Hanćkowiak, Edyta Szymańska, Wojciech Wawrzyniak

Research output: Contribution to journalArticle

Abstract

We consider the problem of matching clients with servers, each of which can process a subset of clients. It is known as the semi-matching or load balancing problem in a bipartite graph G=(V,U,E), where U corresponds to the clients and V to the servers. The goal is to find a set of edges M⊆E such that every vertex in U is incident to exactly one edge in M. The load of a server v∈V is defined as (degM⁡(v)+12), and the problem is to find a semi-matching M that minimizes the sum of the loads of the servers. We show that to find an optimal solution in a distributed setting Ω(|V|) rounds are needed and propose distributed deterministic approximation algorithms for the problem. It yields 2-approximation and has time complexity O(Δ5), where Δ is the maximum degree in V. We also give some greedy algorithms.

Original languageEnglish (US)
Pages (from-to)1251-1267
Number of pages17
JournalJournal of Computer and System Sciences
Volume82
Issue number8
DOIs
StatePublished - Dec 1 2016

Keywords

  • Distributed algorithms
  • Semi-matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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