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Tight bounds for break minimization in tournament scheduling. (English) Zbl 1151.90014

Summary: We consider round-robin sports tournaments with \(n\) teams and \(n - 1\) rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least \(\frac 1 4 n(n-2)\) breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature.

MSC:

90B35 Deterministic scheduling theory in operations research
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References:

[1] de Werra, D., Scheduling in sports, (Ann. Discrete Math., vol. 11 (1981)), 381-395 · Zbl 0469.90042
[2] Post, G.; Woeginger, G. J., Sports tournaments, home-away assignments, and the break minimization problem, Discrete Optim., 3, 165-173 (2006) · Zbl 1146.90517
[3] R.V. Rasmussen, M.A. Trick, Round robin scheduling—A survey, European J. Oper. Res. (2006), in press; R.V. Rasmussen, M.A. Trick, Round robin scheduling—A survey, European J. Oper. Res. (2006), in press · Zbl 1144.90396
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