Maximizing breaks and bounding solutions to the mirrored traveling tournament problem

Authors:
Sebastián Urrutia;Celso C. Ribeiro
Affiliations:
Department of Computer Science, Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil;Department of Computer Science, Universidade Federal Fluminense, Niterói, RJ, Brazil
Venue:
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Year:
2006

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Abstract

We investigate the relation between two aspects of round robin tournament scheduling problems: breaks and distances. The distance minimization problem and the breaks maximization problem are equivalent when the distance between every pair of teams is equal to 1. We show how to construct schedules with a maximum number of breaks for some tournament types. The connection between breaks maximization and distance minimization is used to derive lower bounds to the mirrored traveling tournament problem and to prove the optimality of solutions found by a heuristic for the latter.