Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Traveling Tournament Problem Description and Benchmarks
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A simulated annealing approach to the traveling tournament problem
Journal of Scheduling
A method for combining complementary techniques for document image segmentation
Pattern Recognition
Complexity of the traveling tournament problem
Theoretical Computer Science
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
In many professional sports leagues, teams from opposing leagues/conferences compete against one another, playing inter-league games. This is an example of a bipartite tournament. In this paper, we consider the problem of reducing the total travel distance of bipartite tournaments, by analyzing inter-league scheduling from the perspective of discrete optimization. This research has natural applications to sports scheduling, especially for leagues such as the National Basketball Association (NBA) where teams must travel long distances across North America to play all their games, thus consuming much time, money, and greenhouse gas emissions. We introduce the Bipartite Traveling Tournament Problem (BTTP), the interleague variant of the well-studied Traveling Tournament Problem. We prove that the 2n-team BTTP is NP-complete, but for small values of n, a distance-optimal inter-league schedule can be generated from an algorithm based on minimum-weight 4-cycle-covers. We apply our theoretical results to the 12-team Nippon Professional Baseball (NPB) league in Japan, producing a provably-optimal schedule requiring 42950 kilometres of total team travel, a 16% reduction compared to the actual distance traveled by these teams during the 2010 NPB season. We also develop a nearly-optimal inter-league tournament for the 30-team NBA league, just 3.8% higher than the trivial theoretical lower bound.