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Parallel matching for ranking all teams in a tournament

Part of: Combinatorics Combinatorial probability

Published online by Cambridge University Press:  01 July 2016

Kei Kobayashi ,
Hideki Kawasaki  and
Akimichi Takemura
Kei Kobayashi*
Affiliation:
The Institute of Statistical Mathematics
Hideki Kawasaki*
Affiliation:
The University of Tokyo
Akimichi Takemura*
Affiliation:
The University of Tokyo
*
∗ Postal address: The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan. Email address: [email protected]
∗∗ Postal address: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
∗∗ Postal address: Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
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Abstract

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We propose a simple and efficient scheme for ranking all teams in a tournament where matches can be played simultaneously. We show that the distribution of the number of rounds of the proposed scheme can be derived using lattice path counting techniques used in ballot problems. We also discuss our method from the viewpoint of parallel sorting algorithms.

Keywords

Ballot problemBradley-Terry modelextreme value distributionHasse diagramKolmogorov-Smirnov statisticlattice path countingodd-even mergeparallel sortingpartially ordered set

MSC classification

Primary: 05A16: Asymptotic enumeration 60C05: Combinatorial probability
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 804 - 826
Copyright
Copyright © Applied Probability Trust 2006 

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