On the separation in 2-period double round robin tournaments with minimum breaks

  • Authors:

  • Lishun Zeng;Shinji Mizuno

  • Affiliations:

  • Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Tokyo 152-8552, Japan;Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Tokyo 152-8552, Japan

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

This paper considers the separation in 2-period double round robin tournaments (2P-DRRTs) with minimum breaks. The separation is a lower bound on the number of slots between the two games with the same opponents. None of known schemes provides 2P-DRRTs with minimum breaks and a positive separation. We first propose a new scheme to generate 2-separation 2P-DRRTs with minimum breaks, based on single round robin tournaments (SRRTs) with minimum breaks which have the last break in the third slot from the end. Our experiment results show that such SRRTs exist for 8-68 teams. Secondly, we consider maximizing the separation in general 2P-DRRTs with minimum breaks by integer programming and constraint programming, respectively. The two approaches of direct formulation and ''first-break, then-schedule'' decomposition are presented and compared. We obtain the maximum separation for up to 14 teams. Furthermore, we consider the application with place constraints to show the flexibility and efficiency of scheduling 2P-DRRTs with minimum breaks and a positive separation.