Brief announcement: Distributed approximations for the semi-matching problem

Andrzej Czygrinow, Michal Hanćkowiak, Krzysztof Krzywdziński, Edyta Szymańska, Wojciech Wawrzyniak

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

4 Scopus citations

Abstract

We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to 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 the square of its degree 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. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg M (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ v ε V (deg M (v))2 is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max v ε V d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

Original languageEnglish (US)
Title of host publicationDistributed Computing - 25th International Symposium, DISC 2011, Proceedings
Pages200-201
Number of pages2
DOIs
StatePublished - Nov 2 2011
Event25th International Symposium on Distributed Computing, DISC 2011 - Rome, Italy
Duration: Sep 20 2011Sep 22 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6950 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other25th International Symposium on Distributed Computing, DISC 2011
CountryItaly
CityRome
Period9/20/119/22/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Czygrinow, A., Hanćkowiak, M., Krzywdziński, K., Szymańska, E., & Wawrzyniak, W. (2011). Brief announcement: Distributed approximations for the semi-matching problem. In Distributed Computing - 25th International Symposium, DISC 2011, Proceedings (pp. 200-201). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6950 LNCS). https://doi.org/10.1007/978-3-642-24100-0_18