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Analysis of a Simple Greedy Matching Algorithm on Random Cubic Graphs

Published online by Cambridge University Press:  12 September 2008

Alan Frieze ,
A. J. Radcliffe  and
Stephen Suen
Alan Frieze
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh PA15213, U.S.A.
A. J. Radcliffe
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh PA15213, U.S.A.
Stephen Suen
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh PA15213, U.S.A.
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Abstract

We consider the performance of a simple greedy matching algorithm MINGREEDY when applied to random cubic graphs. We show that if λn is the expected number of vertices not matched by MINGREEDY, there are positive constants c1 and c2 such that C1n1/5 ≤ λn ≤ C2n1/5 log n.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 1 , March 1995 , pp. 47 - 66
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Bender, E. A. and Canfield, E. R. (1978) The asymptotic number of labelled graphs with given degree sequences. Journal of Combinatorial Theory, Series A 24 296–307.Google Scholar
[2]Bollobás, B. (1980) A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. European Journal on Combinatorics 1 311–316.CrossRefGoogle Scholar
[3]Dyer, M. E. and Frieze, A. M. (1991) Randomized greedy matching, Random Structures and Algorithms 2 29–45.Google Scholar
[4]Dyer, M. E., Frieze, A. M. and Pittel, B. (to appear) On the average performance of the greedy matching algorithm.Google Scholar
[5]Goldschmidt, O. and Hochbaum, D. S. (1990) A fast perfect-matching algorithm in random graphs, SIAM Journal on Discrete mathematics, 3 48–57.CrossRefGoogle Scholar
[6]Korte, B. and Hausmann, D. (1978) An analysis of the greedy algorithm for independence systems, In: Alspach, B., Hall, P. and Milles, D. J. (eds.) Algorithmic Aspects of Combinatorics, Annals of Discrete Mathematics, 265–74.CrossRefGoogle Scholar
[7]Karp, R. M. and Sipser, M. (1981) Maximum matchings in sparse random graphs, Proceedings of the 22nd Annual IEEE Symposium on Foundations of Computing 364–375.Google Scholar
[8]Tinhofer, G. (1984) A probabilistic analysis of some greedy cardinality matching algorithms. Annals of Operations Research 1 239–254.CrossRefGoogle Scholar