Tournament Scheduling Research Articles

Applying the Diamond Product of Graphs to the Round Robin Tournament Scheduling Problem

The diamond product of a graph G(V,E) with a graph H(V′,E′) denoted by G⋄H is a graph whose a vertex set V(G⋄H) is a Hom(G,H) and an edge set E(G⋄H)={{f,g}|f,g∈Hom(G,H) and {f(x),g(x)}∈E′, for all x∈V(G)}. A round robin tournament problem involves creating a schedule where each participant plays against every other participant exactly once. This research represents the application of the diamond product of path graph and complete graph to 2n-participants round robin tournament problem. Moreover, the research also represents an algorithm to find a solution of 2n-participants round robin tournament problem.

Tournament schedules and incentives in a double round‐robin tournament with four teams

AbstractIn a round‐robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless matches in a double round‐robin contest with four teams. The probability that such matches arise can serve as a novel fairness criterion to compare and evaluate match schedules. Our approach is illustrated by the UEFA Champions League group stage. A simulation model is built to compare the 12 valid schedules for the group matches. Some schedules are shown to be dominated by other schedules. It is found that the strongest team should play at home in the last round against one of the middle teams, depending on the preferences of the tournament organiser. Choosing an optimal sequence of matches with respect to the proposed metric can help to avoid uninteresting matches.

Fair travel distances in tournament schedules: A cooperative game theory approach

The most studied problem in sports scheduling, so-called traveling tournament problem (TTP), aims at finding schedules minimizing the total distance traveled by the teams. While minimizing all the traveling between games is efficient from the overall perspective, it overlooks the distribution of the travel among the teams. Consequently, some teams may end up better than others with respect to their individual goals, an imbalance which may affect teams’ often-limited resources or preparedness for the games. This article adopts a cooperative game theory framework to obtain tournament schedules where the distances traveled by the teams are allocated according to fairness criteria. The approach consists of three steps. First, the scheduling problem is reformulated as a transferable utility game. Second, by means of well-established allocation methods, an ideal distance distribution among the teams is determined. Third, we introduce fairness measures to produce a schedule which approximately resembles the ideal distribution. We also discuss the case of not pursuing fairness, but rather a compromise between fairness and minimum total distance. We illustrate the approach by a numerical example in one of the classic TTP data instances.

The impossibility of a perfect tournament

Is there a way to determine which tournament format is better than another? Are round-robin tournaments superior to a single-elimination bracket? Using elements from game design, we generalize the existing literature on tournament design and establish metrics to evaluate the effectiveness of different tournament formats. Our approach does not make any assumptions about the sport or game being played, allowing us to analyze tournaments in their basic form. We establish two basic metrics for determining the effectiveness of a tournament schedule: fairness and balance. These metrics follow logically from the purpose of a tournament, which is to determine the best player. We prove an impossibility theorem that most tournament schedules cannot minimize both fairness and balance, including all those used in practice.

PERANCANGAN APLIKASI PENJADWALAN TURNAMEN FUTSAL BERBASIS WEB

Currently, futsal has developed in various cities and regions. Futsal is a soccer game that is usually played indoors with a smaller field size than a football field. In a futsal tournament held in a certain area, the implementation of the tournament system is still done manually. The author designed a web-based futsal tournament scheduling application using the waterfall method. The web created can make it easier for admins to manage tournament data, teams, groups, tournament schedules and results, along with standings. In addition, this website can also produce fast and accurate information about the tournament to be held.

A quest for a fair schedule: The International Young Physicists' Tournament.

The International Young Physicists’ Tournament is an established team-oriented scientific competition between high school students from 37 countries on 5 continents. The competition consists of scientific discussions called Fights. Three or four teams participate in each Fight, while rotating the roles of Presenter, Opponent, Reviewer, and Observer among them. The rules of a few countries require that each team announces in advance three problems they will present at the regional tournament. The task of the organizers is to choose the composition of Fights in such a way that each team presents each of its chosen problems exactly once and within a single Fight no problem is presented more than once. Besides formalizing these feasibility conditions, in this paper we formulate several additional fairness criteria for tournament schedules. We show that the fulfillment of some of them can be ensured by constructing suitable edge colorings in bipartite graphs. To find fair schedules, we propose integer linear programs and test them on real as well as randomly generated data.

Multi-neighborhood simulated annealing for the sports timetabling competition ITC2021

We describe the solver that we developed for the Sports Timetabling Competition ITC2021, a three-stage simulated annealing approach, that makes use of a portfolio of six different neighborhoods. Five of these neighborhoods are taken from the literature on round-robin tournament scheduling, whereas the last one, denoted as PartialSwapTeamsPhased, is a novel contribution and it is specifically designed for the phased version of the problem. We perform a comprehensive and statistically principled tuning procedure to find the best combination of parameters for the competition instances. We dedicate specific focus to evaluate the contribution given by the new neighborhood PartialSwapTeamsPhased, which yielded better results on most phased instances. Overall, the final outcome is that the three-stage simulated annealing solver is able to find a feasible solution on 44 out of 45 instances and ranked second in both the first competition milestone and the final round. We also propose an Integer Linear Programming model implemented in CPLEX, which, unfortunately, did not produce significant results on the instances of the competition.

On Graph-Transversal Designs and Graph-Authentication Codes Based on Mutually Orthogonal Graph Squares

Combinatorial designs have many interesting and genuine wide applications in areas including analysis and design of algorithms, cryptography, analysis and design of experiments, storage system design, tournament scheduling, optical communications, and computer networks to mention just a few areas. In this paper, we are concerned with the transversal designs and authentication codes as direct applications of combinatorial designs. The novelty of the current paper is demonstrated by the fact that it is the first to introduce the transversal designs and authentication codes by the mutually orthogonal graph squares (MOGS); we call them graph-transversal designs and graph-authentication codes, respectively. Here, the major contributions are the constructions of graph-transversal designs and graph-authentication codes based on several classes of graphs. Also, we present several results such as path-transversal designs, cycle-transversal designs, and disjoint unions of stars-transversal designs.

Towards Prevention of Sportsmen Burnout: Formal Analysis of Sub-Optimal Tournament Scheduling

Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the new sports events pose their own unique set of requirements, and demand novel constraints. Specifically talking of the strictly time bound events, ensuring fairness between the different teams in terms of their rest days, traveling, and the number of successive games they play, becomes a difficult task to resolve, and demands attention. In this work, we present a similar situation with a recently played sports event, where a suboptimal schedule favored some of the sides more than the others. We introduce various competitive parameters to draw a fairness comparison between the sides and propose a weighting criterion to point out the sides that enjoyed this schedule more than the others. Furthermore, we use root mean squared error between an ideal schedule and the actual ones for each side to determine unfairness in the distribution of rest days across their entire schedules. The latter is crucial, since successively playing a large number of games may lead to sportsmen burnout, which must be prevented.

Towards an understanding of family travel decision-making processes in the context of youth sport tourism

Youth sport tourism has grown into a distinct travel segment over the past decade. While communities have invested in sport tourism initiatives, building dedicated sports facilities and competing to host tournaments, little academic attention has been paid to understanding the travel planning and decision-making associated with youth sport families. Utilising an inductive approach, the purpose of this study was to examine the processes and decisions parents make in the context of youth sport tourism to facilitate their children's travel sport participation. In-depth interviews were conducted with youth sport parents from the two US states with significant investments in sport tourism: Indiana and Florida. ( n = 15 FL; n = 18 IN). Three themes were identified in the parents' narratives using grounded theory methods, (1) Travel Logistics, (2) Flow-on Tourism, and (3) Tourn-acations. Travel logistics were dominated by decisions over accommodations and transportation with price and team bonding of consideration. A series of barriers and enablers to participation in flow-on tourism were identified including tournament schedules and proximity to tourist attractions. Decisions to create a mini-vacation out of the tournament trip (tourn-acation) were associated with novelty, distance from home, and timing such as tournaments scheduled around national holidays. A model outlining the family travel decision-making process in the context of youth sport tourism is proffered. Recommendations for DMOs leveraging the flow-on tourism associated with youth sport-events are discussed in addition to acknowledging the role of youth sport tourism in post Covid-19 tourism recovery. • Youth sport tourism family travel decision-making model is proposed. • Price and a desire to be with the team shapes decisions over travel logistics. • Flow-on tourism barriers and enablers identified. • Novelty, distance from home, and timing shape tourn-acation propensity.

An Improved Scheduling Algorithm for Cognitive Radio Networks under Different Traffic Patterns

In this paper we propose a spectrum sharing scheduling algorithm for an infrastructure based cognitive radio network. The problem is formulated to allocate channel to the secondary user (SU) based on the idle frequency band, distance, power, bit error rate and SINR. Two scheduling algorithms namely tournament scheduling (TMS) and optimized back–tracking scheduling (OBS) has been developed for the scenario where few primary and many secondary exist in a typical cognitive radio environment. The OBS and TMS algorithm has been implemented and simulated under different traffic patterns namely, Poisson and Pareto over constant bit rate (CBR), variable bit rate (VBR) and best effort services. The simulation result shows a considerable reduction in execution time for the OBS method under varying traffic load.

A new approach based on graph matching and evolutionary approach for sport scheduling problem

The Traveling Tournament Problem (TTP) is concerned with finding a double round-robin tournament schedule that minimizes the total distances traveled by the teams. It has attracted significant interest recently since a favorable TTP schedule can result in significant savings for the league. This paper proposes an original evolutionary algorithm for TTP. We first propose a quick and effective constructive algorithm to construct a Double Round Robin Tournament (DRRT) schedule with low travel cost. We then describe an enhanced genetic algorithm with a new crossover operator to improve the travel cost of the generated schedules. A new heuristic for ordering efficiently the scheduled rounds is also proposed. The latter leads to significant enhancement in the quality of the schedules. The overall method is evaluated on publicly available standard benchmarks and compared with other techniques for TTP and UTTP (Unconstrained Traveling Tournament Problem). The computational experiment shows that the proposed approach could build very good solutions comparable to other state-of-the-art approaches or better than the current best solutions on UTTP. Further, our method provides new valuable solutions to some unsolved UTTP instances and outperforms prior methods for all US National League (NL) instances.

CAN ELO RATINGS BE IMPROVED? A CASE STUDY WITH ELITE CHESS PLAYERS


 
 
 Originally designed as a way to reflect past performance, chess ratings are now widely used to reflect players strength with many important aspects in tournament scheduling, advertising and premium shares. The ELO system has been officially adopted by World Chess Federation (FIDE). We used Bayesian analysis of actual data from elite chess players to fit parametric statistical models that could subsidize proposals for rating system improvement. Although most of the considered options are not new, since based on well known preference models, the use of a weighed likelihood function to emulate dynamic rating systems via Bayesian inference is novel. We compared descriptive ability using marginal likelihood based information criteria. Akaike information criterion was used to compare predictions. Many of the considered options improve on Elo ratings and there is strong evidence that dynamic models considering both white advantage and propensity to draws would result in more accurate systems.
 
 

Innovating Youth Tournament Schedules to Minimize School Absenteeism

Participation in sport has been lauded for the myriad benefits provided to youth who engage. Similarly, attendance in school has been identified as a salient contributor to academic success. Thus, the purpose of the present study was to explore the extent to which participation in youth representative (“rep”) hockey in Ontario contributes to avoidable absences from traditional school contexts. Specifically, empirical data from 104 youth rep hockey tournaments, ranging from AE-AAA competitive levels, and the Tyke (7-year-olds) to Midget (17-year-olds) age ranks, were utilized to meet the study’s first purpose. The second purpose was to present an alternative and innovative way youth sport tournaments could be scheduled to minimize school absenteeism. The results of the current investigation show there is merit to the proposed shift in tournament scheduling. Specifically, more than 42,000 avoidable school absences, from the 104 tournaments sampled, could be mitigated with a simple adjustment to tournament schedules.

Tennis influencers: The player effect on social media engagement and demand for tournament attendance

Understanding the interest of sports fans in professional tennis has valuable operational and marketing implications for tournament organisers, marketeers, player sponsors and the media. In sports, professional tennis in particular, the player effect on social media user engagement is still elusive. Using data from the 2019 Australian Open grand slam period, the authors examine Adler’s (1985) theoretical construct in the context of sports and social media. A social listening tool is used to probe more than 2 million posts and comments mentioning elite male and female tennis players on four major social media channels: Twitter, Facebook, Instagram and YouTube, over the grand slam period. It is shown that the effect of professional tennis players on social media user engagement extends beyond their talent. A selection of players had a strong positive impact on prompting social media activity, even after accounting for factors related to their performance, the tournament rounds in which they were featured and the opponents against whom they played. Furthermore, the connection between social media research and sports economics is considered by examining the relationship between a player’s effects on social media engagement and her/his differential influence on demand for tickets at the Australian Tennis Open. The authors further discuss how the social media star influence can be used, in combination with other quantitative measures, to optimise tennis tournament scheduling, determine player appearance fees and lift participation in the sport.

Solving complex problems using model transformations: from set constraint modeling to SAT instance solving

On the one hand, solvers for the propositional satisfiability problem (SAT) can deal with huge instances composed of millions of variables and clauses. On the other hand, Constraint Satisfaction Problems (CSP) can model problems as constraints over a set of variables with non-empty domains. They require combinatorial search methods as well as heuristics to be solved in a reasonable time.In this article, we present a technique that benefits from both expressive CSP modeling and efficient SAT solving. We model problems as CSP set constraints. Then, a propagation algorithm reduces the domains of variables by removing values that cannot participate in any valid assignment. The reduced CSP set constraints are transformed into a set of suitable SAT instances. They may be simplified by a preprocessing method before applying a standard SAT solver for computing their solutions.The practical usefulness of this technique is illustrated with two well-known problems: a) the Social Golfer, and b) the Sports Tournament Scheduling. We obtained competitive results either compared with ad hoc solvers or with hand-written SAT instances. Compared with direct SAT modeling, the proposed technique offers higher expressiveness, is less error-prone, and is relatively simpler to apply. The automatically generated propositional satisfiability instances are rather small in terms of clauses and variables. Hence, applying the constraint propagation phase, even huge instances of our problems can be tackled and efficiently solved.

Optimization of International Sport Event Tournament Schedules: A Managerial View on The Scheduling Fairness of The World Baseball Softball Confederation Premier 12 Tournament

Optimization of International Sport Event Tournament Schedules: A Managerial View on The Scheduling Fairness of The World Baseball Softball Confederation Premier 12 Tournament

Node embeddings in dynamic graphs

In this paper, we present algorithms that learn and update temporal node embeddings on the fly for tracking and measuring node similarity over time in graph streams. Recently, several representation learning methods have been proposed that are capable of embedding nodes in a vector space in a way that captures the network structure. Most of the known techniques extract embeddings from static graph snapshots. By contrast, modeling the dynamics of the nodes in temporal networks requires evolving node representations. In order to update node representations that reflect the temporal changes in the local graph structure, we rely on ideas for data stream algorithms. For example, we assess neighborhood overlap by a MinHash fingerprint-based algorithm.To evaluate our methods, in addition to the standard link prediction task, we provide dynamic ground truth data for the quantitative evaluation of similarity search by using online updated node embeddings. In our experiments, we constructed tennis tournament Twitter mention graphs as edge streams and compiled dynamic ground truth by using tournament schedule as external source. Our new algorithms outperformed snapshot-based batch methods for both link prediction and similarity search.

Accounting for the warm-up: describing the proportion of total session demands in women’s field hockey – Female Athletes in Motion (FAiM) study

ABSTRACTThis study quantified the proportion and absolute amount of total session demands accounted for by the warm-up during female field hockey matches. A U21 national women’s field hockey team was monitored during eight matches with GPS/heart rate monitors. A RM-ANOVA compared the relative and absolute demands of the warm-up and total session across matches. Differences between matches for warm-up and total session demands occurred. The average warm-up accounted for 27 ± 2% of total distance (~2,500 m of ~9,400 m) and 30 ± 2% of total session duration (~39 min of ~130 min). Distances covered during the warm-up accounted for 30 ± 2 (low), 26 ± 4 (moderate), 9 ± 2 (high), and 6 ± 2% (maximal) of the total session distances. Cumulatively, the warm-up contributed ~10, 9, 0.4, and 0.06 km in the respective velocity bands. The warm-up duration in heart rate zones was 37 ± 3 (50–80% HRpeak), 22 ± 9 (80–90%), and 3 ± 4% (>90%) of the respective total session duration, corresponding to cumulative totals of ~250, 50 and 10 min in each heart rate intensity band. The warm-up represents a substantial proportion of the total session demands; showing a decreasing contribution with increasing intensity. These outcomes are important in the context of monitoring accumulated demands during congested field hockey tournament schedules.

Sport Tournament Automated Scheduling System

The organizer of sport events often facing problems such as wrong calculations of marks and scores, as well as difficult to create a good and reliable schedule. Most of the time, the issues about the level of integrity of committee members and also issues about errors made by human came into the picture. Therefore, the development of sport tournament automated scheduling system is proposed. The system will be able to automatically generate the tournament schedule as well as automatically calculating the scores of each tournament. The problem of scheduling the matches of a round robin and knock-out phase in a sport league are given focus. The problem is defined formally and the computational complexity is being noted. A solution algorithm is presented using a two-step approach. The first step is the creation of a tournament pattern and is based on known graph-theoretic method. The second one is an assignment problem and it is solved using a constraint based depth-first branch and bound procedure that assigns actual teams to numbers in the pattern. As a result, the scheduling process and knock down phase become easy for the tournament organizer and at the same time increasing the level of reliability.