Complexity of Scheduling and Predicting Round-Robin Tournaments.

Tournaments are commonly used to identify winners, for example in sports. We study the computational complexity of problems related to scheduling the matches in a tournament and predicting the outcome with a special focus on round-robin tournaments, which is the most prominent tournament type used in sports. Besides the general financial and intrinsically motivated interest of various agents in tournament prediction, the recently very relevant winner determination for suddenly discontinued tournaments is a strong motivation. We show the immense theoretical complexity of predicting the winners in round-robin tournaments even under the assumption that only three matchdays remain to be played. On the other hand, we present an FPT algorithm and analyze its practical complexity using experiments on real-world and generated data, showing the applicability of the algorithm in praxis. To the best of our knowledge, this is the first exact and not purely brute-force oriented approach for predicting round-robin tournaments.