Minimum Number Of Breaks Research Articles

Fair-fixture: Minimizing carry-over effects in football leagues

<p style='text-indent:20px;'>We study a sports scheduling problem with the objective of minimizing carry-over effects in round robin tournaments.In the first part, focusing on tournaments that allow minimum number of breaks (at most one) for each team, we formulate an integer programming model and provide an efficient heuristic algorithm to solve this computationally expensive problem. We apply the algorithm to the current Turkish Professional Football League and present an alternative scheduling template. In the second part, we discuss how the carry-over effects can be further decreased if the number of breaks is allowed to be of slightly larger value and numerically represent this trade-off.

Constructing fair single round robin tournaments regarding strength groups with a minimum number of breaks

In this paper, we present a constructive method to show the existence of group-balanced single round robin tournaments (SRRTs) with a minimum number of breaks, if the number of groups is a power of 2 with identical even group sizes. When the number of teams is a multiple of 4, we show the existence of group-changing SRRTs with a minimum number of breaks, if the union of some groups contains exactly half of the teams.

ON THE GENERALIZED MIRRORED SCHEME FOR DOUBLE ROUND ROBIN TOURNAMENTS IN SPORTS SCHEDULING

In this paper we propose the generalized mirrored scheme for scheduling double round robin tournaments (DRRTs), a common topic in sports scheduling, to deal with the conflicting constraints of breaks and separation. In practice, usually a small number of breaks and a large separation are desirable, but typical methods of scheduling DRRTs cannot obtain both a minimum number of breaks and a positive separation. We firstly consider DRRTs by this scheme with a separation of two slots and a minimum number of breaks. In case the number of teams is a multiple of four, we show that such DRRTs could be generated by a constructive method; we also propose a model and find such DRRTs for any other numbers of teams up to 90. Secondly, we consider those with a separation of more than two. We show that if a minimum number of breaks is required, DRRTs with a separation of any number of slots could be obtained by a constructive method, for some large number of teams; otherwise, a tradeoff for a large separation at the cost of only four additional breaks exists for any number of teams.

A branching scheme for minimum cost tournaments with regard to real-world constraints

Single round robin tournaments are a well-known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated with each possible match. Moreover, stadium availability, fixed matches, and regions’ capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasible with regard to these additional constraints. A branching scheme is developed where branching is done by fixing a break for a team. Thus, the focus is on identifying breaks leading to an infeasible home away pattern set in order to avoid the resulting infeasible subtrees of a branch and bound tree.

Using a SAT-solver to schedule sports leagues

Tournament schedules of sports leagues have to satisfy several types of constraints such as stadium unavailability, fixed matches, forbidden matches, minimum number of breaks. Usually, there is no schedule satisfying all given constraints and, hence, some of the constraints are considered as `soft' ones. There are various models appropriately describing the environment of sport leagues. Only heuristic methods are known from the literature for solving instances of real life dimensions. We consider here a model which satisfies the demands of many sports leagues. We solve our model by reduction to series of instances of the propositional satisfiability problem and adaption of a satisfiability solver for these specific instances. We test our method on two real life examples and solve the problem optimally within our model in each case. Our solver shows good computational results also on generated test instances, which are motivated by real life requirements. It can be easily extended to meet the demands of other sports leagues.

Constructing fair round robin tournaments with a minimum number of breaks

Given n clubs with two teams each, we show that, if n is even, it is possible to construct a schedule for a single round robin tournament satisfying the following properties: the number of breaks is 2 n − 2 , teams of the same club never play at home simultaneously, and they play against each other in the first round. We also consider a fairness constraint related to different playing strengths of teams competing in the tournament.

A branching scheme for finding cost-minimal round robin tournaments

Single round robin tournaments are a well known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated to each possible match. The goal is to find the minimum cost tournament among those having the minimum number of breaks. We pick up structural properties of home–away-pattern sets having the minimum number of breaks. A branching idea using these properties is developed in order to guide branching steps on the first levels of a branch-and-bound tree in order to avoid nodes corresponding to infeasible subproblems.

Minimizing costs in round robin tournaments with place constraints

In this paper we consider a general sports league scheduling problem and propose solution algorithms for it. The objective is to find a feasible schedule for a round robin tournament with minimum number of breaks and minimum total costs where additionally place constraints are taken into account. We present a “first-break, then-schedule” approach which uses an enumerative procedure to generate home-away patterns and integer programming for finding corresponding schedules. Computational results are presented for leagues with up to 14 teams.

A branch-and-price algorithm for scheduling sport leagues

A single round robin tournament can be described as a league of a set T of n teams (n even) to be scheduled such that each team plays exactly once against each other team and such that each team plays exactly once per period resulting in a set P of n−1 periods. Matches are carried out at one of the stadiums of both opponents. A team playing twice at home or twice away in two consecutive periods is said to have a break in the latter of both periods. There is a vast field of requests arising in real-world problems. For example, the number of breaks is to be minimized due to fairness reasons. It is well known that at least n−2 breaks must occur. We focus on schedules having the minimum number of breaks. Costs corresponding to each possible match are given and the objective is to minimize the sum of cost of arranged matches. Then, sports league scheduling can be seen as a hard combinatorial optimization problem. We develop a branch-and-price approach in order to find optimal solutions.

Insights into the sites of X ray and neutron induced chromosomal aberrations in human lymphocytes using COBRA-MFISH.

A multi-colour fluorescence in situ hybridisation (MFISH) assay has been developed, for simultaneous visualisation of all human chromosomes in 24 different colours. This assay is based on the simultaneous use of combinatorial labelling and ratio labelling, the so called combined binary ratio labelling (COBRA). This technique is used to study the spectra of chromosomal exchanges induced by X ray and neutrons in human lymphocytes. With X rays the dose-effect relationships for both dicentrics and translocations were linear-quadratic, whereas with neutrons these were linear. Among aberrant cells, average estimates of the minimum number of breaks was higher for neutrons than for X rays. Moreover, the induced chromosomal exchange patterns were more complex following neutron irradiation in comparison with X rays. COBRA-MFISH was found to have a greater resolving power over partial labelling for the accurate detection of complex translocations and insertions. With neutrons the frequencies of both were higher than those induced by X rays, and their relative proportions to the total frequencies were independent of dose. These data suggest insertions can be used as the 'signature' of high LET radiation.

Some models of graphs for scheduling sports competitions

Graph-theoretical models are given for constructing the season schedule of a sports league; we consider in particular the problem of having an alternation of home-games and away-games which is as regular as possible, and we characterize schedules with a minimum number of breaks in the alternations. Some related graph-theoretical properties are discussed and a solvable case with preassignments of home-games and away-games is presented.

Minimizing irregularities in sports schedules using graph theory

Some combinatorial problems occurring in scheduling the games of a sports league are presented; solutions are obtained by constructing oriented factorisations of complete graphs. One considers schedules with a minimum number of breaks in the sequences of home-games and away-games and schedules with minimum number of days with breaks. Some open problems are also mentioned.

Minimizing irregularities in sports schedules using graph theory

Abstract Some combinatorial problems occurring in scheduling the games of a sports league are presented; solutions are obtained by constructing oriented factorisations of complete graphs. One considers schedules with a minimum number of breaks in the sequences of home-games and away-games and schedules with minimum number of days with breaks. Some open problems are also mentioned.