Abstract
We study competitions structured as hierarchically shaped single-elimination tournaments. We define optimal tournaments by maximizing attractiveness such that the topmost players will have the chance to meet in higher stages of the tournament. We propose a dynamic programming algorithm for computing optimal tournaments and we provide its sound complexity analysis. Based on the idea of the dynamic programming approach, we also develop more efficient deterministic and stochastic sub-optimal algorithms. We present experimental results obtained with the Python implementation of all the proposed algorithms regarding the optimality of solutions and the efficiency of the running time.
Highlights
Tournament design is a combinatorial problem with many theoretical implications, as well as with a lot of practical applications
Players are assigned to each leaf of the tournament tree; as we can argue that this method of tournament design has some limitations, we proposed different “integrated” approach
The optimality criterion aimed to maximize tournament attractiveness by letting the topmost players meet in higher stages of the tournament
Summary
Tournament design is a combinatorial problem with many theoretical implications, as well as with a lot of practical applications. There are two main principles used in tournament design: “round-robin” principle and “knockout” principle They can be used in isolation or combined for obtaining different tournaments designs, depending on various factors, such as the number of players, time available to carry out the tournament, and application domain. If there is a number N of players equal to a power of 2, for example N = 8 = 23 the tournament tree is a complete binary tree with all the players entering the tournament in the first round; in the general case, the number of players might not be a power of 2, for example N = 9. 3. An exact dynamic programming algorithm for computing optimal tournaments in the general case. The implementation issues of the proposed algorithms using Python, as well as the experimental results obtained with our implementation
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