On the application of graph colouring techniques in round-robin sports scheduling

The purpose of this paper is twofold. First, it explores the issue of producing valid, compact round-robin sports schedules by considering the problem as one of graph colouring. Using this model, which can also be extended to incorporate additional constraints, the difficulty of such problems is then gauged by considering the performance of a number of different graph colouring algorithms. Second, neighbourhood operators are then proposed that can be derived from the underlying graph colouring model and, in an example application, we show how these operators can be used in conjunction with multi-objective optimisation techniques to produce high-quality solutions to a real-world sports league scheduling problem encountered at the Welsh Rugby Union in Cardiff, Wales

A wide-ranging computational comparison of high-performance graph colouring algorithms

This paper reviews the current state of the literature surrounding methods for the general graph colouring problem and presents a broad comparison of six high-performance algorithms, each belonging to one of the main algorithmic schemes identified. Unlike many previous computational studies in graph colouring, a large range of both artificially generated and real-world graphs are considered, culminating in over 40,000 individual trials that have consumed more than a decade of computation time in total. The picture painted by the comparison is complex, with each method outperforming all others on at least one occasion; however, general patterns are also observed, particularly with regards to the advantages of hybridising local-search techniques with global-based operators

A Survey of League Championship Algorithm: Prospects and Challenges

The League Championship Algorithm (LCA) is sport-inspired optimization algorithm that was introduced by Ali Husseinzadeh Kashan in the year 2009. It has since drawn enormous interest among the researchers because of its potential efficiency in solving many optimization problems and real-world applications. The LCA has also shown great potentials in solving non-deterministic polynomial time (NP-complete) problems. This survey presents a brief synopsis of the LCA literatures in peer-reviewed journals, conferences and book chapters. These research articles are then categorized according to indexing in the major academic databases (Web of Science, Scopus, IEEE Xplore and the Google Scholar). The analysis was also done to explore the prospects and the challenges of the algorithm and its acceptability among researchers. This systematic categorization can be used as a basis for future studies.Comment: 10 pages, 2 figures, 2 tables, Indian Journal of Science and Technology, 201

An instance data repository for the round-robin sports timetabling problem

The sports timetabling problem is a combinatorial optimization problem that consists of creating a timetable that defines against whom, when and where teams play games. This is a complex matter, since real-life sports timetabling applications are typically highly constrained. The vast amount and variety of constraints and the lack of generally accepted benchmark problem instances make that timetable algorithms proposed in the literature are often tested on just one or two specific seasons of the competition under consideration. This is problematic since only a few algorithmic insights are gained. To mitigate this issue, this article provides a problem instance repository containing over 40 different types of instances covering artificial and real-life problem instances. The construction of such a repository is not trivial, since there are dozens of constraints that need to be expressed in a standardized format. For this, our repository relies on RobinX, an XML-supported classification framework. The resulting repository provides a (non-exhaustive) overview of most real-life sports timetabling applications published over the last five decades. For every problem, a short description highlights the most distinguishing characteristics of the problem. The repository is publicly available and will be continuously updated as new instances or better solutions become available

Prior analysis and scheduling of the 2011 Rugby Union ITM Cup in New Zealand.

This paper describes work done for the New Zealand Rugby Union (NZRU) in preparation for their most important wholly domestic competition in 2011. This competition had to be played during a shorter timescale than usual because of the 2011 Rugby Union World Cup, and the NZRU were keen to ensure that they could incorporate the format they wanted into this timescale without unfortunate consequences. In addition, they wanted to introduce a novel feature into this tournament. Thus some detailed prior experimental, or "what-if", analysis was necessary. This paper describes this analysis and its results. As a result of this analysis, the NZRU was persuaded to abandon one of its design ideas, but was able to proceed with others, enabling them to announce the detailed format of the competition in the confidence that it would work well in practice. Subsequent scheduling of the competition in this format proved successful, and the resulting schedule is shown together with detailed analysis of its notional costs. The paper demonstrates how important it can be for schedulers to be closely involved in tournament design in advance of the actual scheduling

A Greedy Algorithm for the Social Golfer and the Oberwolfach Problem

Inspired by the increasing popularity of Swiss-system tournaments in sports, we study the problem of predetermining the number of rounds that can be guaranteed in a Swiss-system tournament. Matches of these tournaments are usually determined in a myopic round-based way dependent on the results of previous rounds. Together with the hard constraint that no two players meet more than once during the tournament, at some point it might become infeasible to schedule a next round. For tournaments with $n$ players and match sizes of $k\geq2$ players, we prove that we can always guarantee $\lfloor \frac{n}{k(k-1)} \rfloor$ rounds. We show that this bound is tight. This provides a simple polynomial time constant factor approximation algorithm for the social golfer problem. We extend the results to the Oberwolfach problem. We show that a simple greedy approach guarantees at least $\lfloor \frac{n+4}{6} \rfloor$ rounds for the Oberwolfach problem. This yields a polynomial time $\frac{1}{3+\epsilon}$-approximation algorithm for any fixed $\epsilon>0$ for the Oberwolfach problem. Assuming that El-Zahar's conjecture is true, we improve the bound on the number of rounds to be essentially tight.Comment: 24 pages, 4 figure