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Combinatorial properties of strength groups in round robin tournaments

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  • Briskorn, Dirk

Abstract

A single round robin tournament (RRT) consists of a set T of n teams (n even) and a set P of n - 1 periods. The teams have to be scheduled such that each team plays exactly once against each other team and such that each team plays exactly once per period. In order to establish fairness among teams we consider a partition of teams into strength groups. Then, the goal is to avoid a team playing against extremely weak or extremely strong teams in consecutive periods. We propose two concepts ensuring different degrees of fairness. One question arising here is whether a single RRT exists for a given number of teams n and a given partition of the set of teams into strength groups or not. In this paper we examine this question. Furthermore, we analyse the computational complexity of cost minimization problems in the presence of strength group requirements.

Suggested Citation

  • Briskorn, Dirk, 2009. "Combinatorial properties of strength groups in round robin tournaments," European Journal of Operational Research, Elsevier, vol. 192(3), pages 744-754, February.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:744-754
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    Cited by:

    1. Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre (Ed.), 2010. "Jahresbericht 2009," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 650, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Larson Jeffrey & Johansson Mikael, 2014. "Constructing schedules for sports leagues with divisional and round-robin tournaments," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 1-11, June.
    3. David Van Bulck & Dries Goossens & Jo¨rn Scho¨nberger & Mario Guajardo, 2020. "An Instance Data Repository for the Round-robin Sports Timetabling Problem," Management and Labour Studies, XLRI Jamshedpur, School of Business Management & Human Resources, vol. 45(2), pages 184-200, May.
    4. Tasbih Tuffaha & Burak Çavdaroğlu & Tankut Atan, 2023. "Round-robin scheduling with regard to rest differences," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 269-301, July.
    5. van 't Hof, Pim & Post, Gerhard & Briskorn, Dirk, 2009. "Round-robin tournaments with minimum number of breaks and two teams per club," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 648, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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