Who Can Win a Single-Elimination Tournament?

A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that their favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that \emph{every} player in an $n$ player tournament generated by the Condorcet Random Model will be an SE winner even when the noise is as small as possible, $p=\Theta(\ln n/n)$; prior work only had such results for $p\geq \Omega(\sqrt{\ln n/n})$. We also establish new results for significantly more general generative models.Comment: A preliminary version appeared in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), 201

Particle Swarm Algorithm for Improved Handling of the Mirrored Traveling Tournament Problem

In this study, we used a particle swarm optimization (PSO) algorithm to address a variation of the non-deterministic polynomial-time NP-hard traveling tournament problem, which determines the optimal schedule for a double round-robin tournament, for an even number of teams, to minimize the number of trips taken. Our proposed algorithm iteratively explored the search space with a swarm of particles to find near-optimal solutions. We also developed three techniques for updating the particle velocity to move towards optimal points, which randomly select and replace row and column parameters to find candidate positions close to an optimal solution. To further optimize the solution, we calculated the particle cost function, an important consideration within the problem conditions, for team revenues, fans, and media. We compared our computation results with two well-known meta-Heuristics: a genetics algorithm utilizing a swapping method and a Greedy Randomized Adaptive Search Procedure Iterated Local Search algorithm heuristic on a set of 20 teams. Ultimately, the PSO algorithm generated solutions that were comparable, and often superior, to the existing well-known solutions. Our results indicate that our proposed algorithm could aid in reducing the overall budget expenditures of international sports league organizations, which could enable significant monetary savings and increase profit margins

Scheduling a non-professional indoor football league : a tabu search based approach

This paper deals with a real-life scheduling problem of a non-professional indoor football league. The goal is to develop a schedule for a time-relaxed, double round-robin tournament which avoids close successions of games involving the same team in a limited period of time. This scheduling problem is interesting, because games are not planned in rounds. Instead, each team provides time slots in which they can play a home game, and time slots in which they cannot play at all. We present an integer programming formulation and a heuristic based on tabu search. The core component of this algorithm consists of solving a transportation problem, which schedules (or reschedules) all home games of a team. Our heuristic generates schedules with a quality comparable to those found with IP solvers, however with considerably less computational effort. These schedules were approved by the league organizers, and used in practice for the seasons 2009-2010 till 2016-2017

Tailoring a psychophysiologically driven rating system

Humans have always been interested in ways to measure and compare their performances to establish who is best at a particular activity. The first Olympic Games, for instance, were carried out in 776 BC, and it was a defining moment in history where ranking based competitive activities managed to reach the general populous. Every competition must face the issue of how to evaluate and rank competitors, and often rules are required to account for many different aspects such as variations in conditions, the ability to cheat, and, of course, the value of entertainment. Nowadays, measurements are performed out through various rating systems, which considers the outcomes of the activity to rate the participants. However, they do not seem to address the psychological aspects of an individual in a competition. This dissertation employs several psychophysiological assessment instruments intending to facilitate the acquisition of skill level rating in competitive gaming. To do so, an exergame that uses non-conventional inputs, such as body tracking to prevent input biases, was developed. The sample size of this study is ten, and the participants were put on a round-robin tournament to provide equal intervals between games for each player. After analyzing the outcome of the competition, it revealed some critical insights on the psychophysiological instruments; Especially the significance of Flow in terms of the prolificacy of a player. Although the findings did not provide an alternative for the traditional rating systems, it shows the importance of considering other aspects of the competition, such as psychophysiological metrics to fine-tune the rating. These potentially reveal more in-depth insight into the competition in comparison to just the binary outcome

Handling fairness issues in time-relaxed tournaments with availability constraints

Sports timetables determine who will play against whom, where, and on which time slot. In contrast to time-constrained sports timetables, time-relaxed timetables utilize (many) more time slots than there are games per team. This offers time-relaxed timetables additional flexibility to take into account venue availability constraints, stating that a team can only play at home when its venue is available, and player availability constraints stating that a team can only play when its players are available. Despite their flexibility, time-relaxed timetables have the drawback that the rest period between teams’ consecutive games can vary considerably, and the difference in the number of games played at any point in the season can become large. Besides, it can be important to timetable home and away games alternately. In this paper, we first establish the computational complexity of time-relaxed timetabling with availability constraints. Naturally, when one also incorporates fairness objectives on top of availability, the problem becomes even more challenging. We present two heuristics that can handle these fairness objectives. First, we propose an adaptive large neighborhood method that repeatedly destroys and repairs a timetable. Second, we propose a memetic algorithm that makes use of local search to schedule or reschedule all home games of a team. For numerous artificial and real-life instances, these heuristics generate high-quality timetables using considerably less computational resources compared to integer programming models solved using a state-of-the-art solver