Generating Approximate Solutions to the TTP using a Linear Distance Relaxation

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 congruent to 4 modulo 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 + epsilon 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.

Authors

• 2 publications
• 28 publications
• Scheduling Bipartite Tournaments to Minimize Total Travel Distance

In many professional sports leagues, teams from opposing leagues/confere...
01/16/2014 ∙ by Richard Hoshino, et al. ∙ 0

• Scheduling Asynchronous Round-Robin Tournaments

We study the problem of scheduling asynchronous round-robin tournaments....
04/11/2018 ∙ by Warut Suksompong, et al. ∙ 0

• An Exact Approach for the Balanced k-Way Partitioning Problem with Weight Constraints and its Application to Sports Team Realignment

In this work a balanced k-way partitioning problem with weight constrain...
09/05/2017 ∙ by Diego Recalde, et al. ∙ 0

• Non-signaling Approximations of Stochastic Team Problems

In this paper, we consider non-signaling approximation of finite stochas...
05/17/2019 ∙ by Naci Saldı, et al. ∙ 0

• An interacting replica approach applied to the traveling salesman problem

We present a physics inspired heuristic method for solving combinatorial...
06/27/2014 ∙ by Bo Sun, et al. ∙ 0

• Hardness Amplification of Optimization Problems

In this paper, we prove a general hardness amplification scheme for opti...
08/27/2019 ∙ by Elazar Goldenberg, et al. ∙ 0

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.