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  Matching Algorithms Are Fast in Sparse Random Graphs

Bast, H., Mehlhorn, K., Schäfer, G., & Tamaki, H. (2004). Matching Algorithms Are Fast in Sparse Random Graphs. In 21st Annual Symposium on Theoretical Aspects of Computer Science (STACS-04) (pp. 81-92). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-290E-8 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2910-D
Genre: Conference Paper

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 Creators:
Bast, Holger1, Author           
Mehlhorn, Kurt1, Author           
Schäfer, Guido1, Author           
Tamaki, Hisao1, Author           
Diekert, Volker, Editor
Habib, Michel, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every nonmaximum matching has an augmenting path of length O(log n). This implies that augmenting path algorithms like the Hopcroft Karp algorithm for bipartite graphs and the Micali Vazirani algorithm for general graphs, which have a worst case running time of O(mpn), run in time O(mlog n) with high probability, where m is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least ln(n) [Average Case Analysis of Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6), 1994]. Our results hold, if only the average degree is a large enough constant. At the same time we simplify the analysis of Motwani.

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Language(s): eng - English
 Dates: 2005-05-232004
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 231169
Other: Local-ID: C1256428004B93B8-1F79D167AE1C3869C1256F9500480213-bast04stacs
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Title: Untitled Event
Place of Event: Montpellier, France
Start-/End Date: 2004-03-25

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Title: 21st Annual Symposium on Theoretical Aspects of Computer Science (STACS-04)
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 81 - 92 Identifier: ISBN: 3-540-21236-1

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 2996 Sequence Number: - Start / End Page: - Identifier: -