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 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages200-201
Number of pages2
Volume6950 LNCS
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Matching Problem
Bipartite Graph
Servers
Server
Costs
Approximation
Subgraph
Minimise
Arbitrary
Vertex of a graph
Theorem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Czygrinow, A., Hanćkowiak, M., Krzywdziński, K., Szymańska, E., & Wawrzyniak, W. (2011). Brief announcement: Distributed approximations for the semi-matching problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6950 LNCS, 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

Brief announcement : Distributed approximations for the semi-matching problem. / Czygrinow, Andrzej; Hanćkowiak, Michal; Krzywdziński, Krzysztof; Szymańska, Edyta; Wawrzyniak, Wojciech.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6950 LNCS 2011. p. 200-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6950 LNCS).

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

Czygrinow, A, Hanćkowiak, M, Krzywdziński, K, Szymańska, E & Wawrzyniak, W 2011, Brief announcement: Distributed approximations for the semi-matching problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6950 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6950 LNCS, pp. 200-201, 25th International Symposium on Distributed Computing, DISC 2011, Rome, Italy, 9/20/11. https://doi.org/10.1007/978-3-642-24100-0_18
Czygrinow A, Hanćkowiak M, Krzywdziński K, Szymańska E, Wawrzyniak W. Brief announcement: Distributed approximations for the semi-matching problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6950 LNCS. 2011. p. 200-201. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-24100-0_18
Czygrinow, Andrzej ; Hanćkowiak, Michal ; Krzywdziński, Krzysztof ; Szymańska, Edyta ; Wawrzyniak, Wojciech. / Brief announcement : Distributed approximations for the semi-matching problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6950 LNCS 2011. pp. 200-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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