• Corpus ID: 238407964

Complexity of Traveling Tournament Problem with Trip Length More Than Three

@article{Chatterjee2021ComplexityOT,
  title={Complexity of Traveling Tournament Problem with Trip Length More Than Three},
  author={Diptendu Chatterjee},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.02300}
}
The Traveling Tournament Problem is a sports-scheduling problem where the goal is to minimize the total travel distance of teams playing a double round-robin tournament. The constraint k is an imposed upper bound on the number of consecutive home or away matches. It is known that TTP is NP-Hard for k = 3 as well as k = ∞. In this work, the general case has been settled by proving that TTP-k is NP-Complete for any fixed k > 3. 

Figures from this paper

References

SHOWING 1-10 OF 22 REFERENCES
Complexity of the Unconstrained Traveling Tournament Problem
Complexity of the traveling tournament problem
Approximating the Traveling Tournament Problem with Maximum Tour Length 2
TLDR
This work considers the traveling tournament problem, which is a well-known benchmark problem in tournament timetabling, and presents an approximation algorithm that has an approximation ratio of 3/2+ 6-4, where n is the number of teams in the tournament.
The Traveling Tournament Problem Description and Benchmarks
TLDR
The Traveling Tournament Problem is a sports timetabling problem that abstracts two issues in creating timetables: home/away pattern feasibility and team travel, and one way of modeling it is described.
An Improved Approximation Algorithm for the Traveling Tournament Problem with Maximum Trip Length Two
TLDR
This paper gives a practical approximation algorithm for the Traveling Tournament Problem, that generates feasible schedules based on minimum perfect matchings in the underlying graph, and can beat all previously-known results of instances with n being a multiple of 4 by 3% to 10%.
A composite-neighborhood tabu search approach to the traveling tournament problem
TLDR
This work proposes a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures and shows that the algorithm is competitive with those in the literature.
A 5.875-approximation for the Traveling Tournament Problem
TLDR
An algorithm which approximates the optimal solution by a factor of 2+2k/n-k/(n−1)+3/n+3/(2⋅k) which is not more than 5.875 for any choice of k≥4 and n≥6 is proposed, the first constant factor approximation for k>3.
Solving the Travelling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach
TLDR
This paper presents the first provably optimal solution for an instance of eight teams of the Travelling Tournament Problem using a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solving the pricing problem.
An Improved Approximation Algorithm for the Traveling Tournament Problem
TLDR
An approximation algorithm is proposed for the traveling tournament problem with the constraints such that both the number of consecutive away games and that of consecutive home games are at most k.
An approximation algorithm for the traveling tournament problem
TLDR
A new lower bound for the traveling tournament problem is proposed, and a randomized approximation algorithm is constructed yielding a feasible solution whose approximation ratio is less than 2+(9/4)/(n−1), where n is the number of teams.
...
...