Single elimination tournament design using dynamic programming algorithm

Abstract

Finding the best single-elimination tournament design is important in scientific inquiry because it can have major financial implications for event organizers and participants. This research aims to create an optimal single-elimination tournament design using binary tree modeling with dummy techniques. Dynamic programming algorithms have been used to compute optimal single-elimination designs to overcome this effectively. This research method uses various implementations of sub-optimal algorithms and then compares their performance in terms of runtime and optimality as a solution to measure the comparison of sub-algorithms. This research shows that the difference in relative costs produced by various sub-algorithms with the same input is quite low. This is expected because quotes are generated as integer values from a small interval 1, ≤ 9, whereas costs tend to reach much higher values. From the comparison of these sub-algorithms, the best results among the sub-optimal algorithms were obtained in the Sub Optimal algorithm 3. We present the experimental findings achieved using the Python implementation of the suggested algorithm, with a focus on the best single-elimination tournament design solution.