ON THE GENERALIZED MIRRORED SCHEME FOR DOUBLE ROUND ROBIN TOURNAMENTS IN SPORTS SCHEDULING

In this paper we propose the generalized mirrored scheme for scheduling double round robin tournaments (DRRTs), a common topic in sports scheduling, to deal with the conflicting constraints of breaks and separation. In practice, usually a small number of breaks and a large separation are desirable, but typical methods of scheduling DRRTs cannot obtain both a minimum number of breaks and a positive separation. We firstly consider DRRTs by this scheme with a separation of two slots and a minimum number of breaks. In case the number of teams is a multiple of four, we show that such DRRTs could be generated by a constructive method; we also propose a model and find such DRRTs for any other numbers of teams up to 90. Secondly, we consider those with a separation of more than two. We show that if a minimum number of breaks is required, DRRTs with a separation of any number of slots could be obtained by a constructive method, for some large number of teams; otherwise, a tradeoff for a large separation at the cost of only four additional breaks exists for any number of teams.