A Computational Study of Problems in Sports

This thesis examines three computational problems in sports. The first problem addressed is determining the minimum number of points needed to guarantee qualification for the playoffs and the minimum number of points needed to have a possibility of qualification for the playoffs of the National Hockey League (NHL). The problem is solved using a phased approach that incrementally adds more complicated tie-breaking constraints if a solution is not found. Each of the phases is solved using a combination of network flows, enumeration and constraint programming. The experimental results show that the solver efficiently solves instances at any point of the season. The second problem addressed is determining the complexity, either worst-case theoretical or practical, of manipulation strategies in sports tournaments. The two most common types of competitions, cups and round robins, are considered and it is shown that there exists a number of polynomial time algorithms for finding manipulation strategies in basic cups and round robins as well as variants. A different type of manipulation, seeding manipulation, is examined from a practical perspective. While the theoretical worst-case complexity remains open, this work shows that, at least on random instances, seeding manipulation even with additional restrictions remains practically manipulable. The third problem addressed is determining whether manipulation strategies can be detected if they were executed in a real tournament. For cups and round robins, algorithms are presented which identify whether a coalition is manipulating the tournament with high accuracy. For seeding manipulation, it is determined that even with many different restrictions it is difficult to determine if manipulation has occurred.