Distributed 2-Approximation Algorithm for the Semi-matching Problem

Andrzej Czygrinow, Michal Hanćkowiak, Edyta Szymańska, Wojciech Wawrzyniak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

In this paper 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, V to the servers, and E is the set of available connections between them. 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 ε V is defined as (d M (v)+1/2) where d M (v) is the degree of v in M, and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. An optimal solution can be found sequentially in polynomial time but the distributed complexity is not well understood. Our algorithm yields (1 + 1/α)-approximation (where α = max{1, 1/2 (|U|/|V| + 1)}) and has time complexity O(Δ 5), where Δ is the maximum degree of a vertex in V. In particular, for Δ = O(1) it gives constant approximation with constant time complexity. We also give a fast algorithm for the case when Δ is large and the degrees in V and U satisfy some additional properties. Both algorithms are deterministic.

Original languageEnglish (US)
Title of host publicationDistributed Computing - 26th International Symposium, DISC 2012, Proceedings
Pages210-222
Number of pages13
DOIs
StatePublished - Nov 9 2012
Event26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil
Duration: Oct 16 2012Oct 18 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7611 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th International Symposium on Distributed Computing, DISC 2012
CountryBrazil
CitySalvador
Period10/16/1210/18/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Czygrinow, A., Hanćkowiak, M., Szymańska, E., & Wawrzyniak, W. (2012). Distributed 2-Approximation Algorithm for the Semi-matching Problem. In Distributed Computing - 26th International Symposium, DISC 2012, Proceedings (pp. 210-222). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS). https://doi.org/10.1007/978-3-642-33651-5_15