The Traveling Tournament Problem Description and Benchmarks
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A method for combining complementary techniques for document image segmentation
Pattern Recognition
Constructive algorithms for the constant distance traveling tournament problem
PATAT'06 Proceedings of the 6th international conference on Practice and theory of automated timetabling VI
Complexity of the traveling tournament problem
Theoretical Computer Science
Scheduling bipartite tournaments to minimize total travel distance
Journal of Artificial Intelligence Research
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In some domestic professional sports leagues, the home stadiums are located in cities connected by a common train line running in one direction. For these instances, we can incorporate this geographical information to determine optimal or nearly-optimal solutions to the n-team Traveling Tournament Problem (TTP), an NP-hard sports scheduling problem whose solution is a double round-robin tournament schedule that minimizes the sum total of distances traveled by all n teams. We introduce the Linear Distance Traveling Tournament Problem (LD-TTP), and solve it for n = 4 and n = 6, generating the complete set of possible solutions through elementary combinatorial techniques. For larger n, we propose a novel "expander construction" that generates an approximate solution to the LD-TTP. For n Ξ 4 (mod 6), we show that our expander construction produces a feasible double round-robin tournament schedule whose total distance is guaranteed to be no worse than 4/3 times the optimal solution, regardless of where the n teams are located. This 4/3 -approximation for the LD-TTP is stronger than the currently best-known ratio of 5/3 + ε for the general TTP. We conclude the paper by applying this linear distance relaxation to general (non-linear) n-team TTP instances, where we develop fast approximate solutions by simply "assuming" the n teams lie on a straight line and solving the modified problem. We show that this technique surprisingly generates the distance-optimal tournament on all benchmark sets on 6 teams, as well as close-to-optimal schedules for larger n, even when the teams are located around a circle or positioned in three-dimensional space.