An exact approach for the balanced k-way partitioning problem with weight constraints and its application to sports team realignment

Abstract

In this work a balanced k-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according to some regulations, where the total distance of the road trips that all teams must travel to play a Double Round Robin Tournament in each group is minimized. Two integer programming formulations for this problem are introduced, and the validity of three families of inequalities associated to the polytope of these formulations is proved. The performance of a tabu search procedure and a Branch & Cut algorithm, which uses the valid inequalities as cuts, is evaluated over simulated and real-world instances. In particular, an optimal solution for the realignment of the Ecuadorian Football league is reported and the methodology can be suitable adapted for the realignment of other sports leagues.

Research on Sports Balanced Development Evaluation System Based on Edge Computing and Balanced Game

“…After entering university, with the increase of age, the mental state of sports slacking appears. ey think that physical education is a supplementary lesson, supporting roles, and nothing more than running, voting, and jumping in the stadium, so it is better to sit down and read more books [16]. It is important to teach culture lessons well; some students are addicted to the network for a long time, and they are averse to taking part in sports activities; some students are afraid of being dirty and tired, they are not interested in many teaching contents and have not formed the correct concept of sports [17].…”

Multi-league sports scheduling with different leagues sizes

“…This problem is known as the sports team grouping problem (Toffolo et al, 2019), or the sports team realignment problem (e.g. Saltzman and Bradford (1996), Mitchell (2003), Ji and Mitchell (2005), Recalde et al (2018)). In order to avoid collusion and match-fixing, league organizers strive to compose leagues such that they have at most one team per club (e.g.…”

Faster algorithms for k-subset sum and variations

“…k-Subset Sum finds applications in a variety of fields, including, but not limited to, scheduling and (fair) resource allocation (Schreiber et al 2018), sports team realignment (Recalde et al 2018), as well as balanced control and treatment group formation for medical studies, focus groups for market research, and controlled sampling for opinion polling. Furthermore, since it generalises several subset sum problems, such as k-way Number Partitioning and Multiple Subset Sum, by enforcing cardinality constraints, one could use it to solve a number of other meaningful problems (Tsai 1992).…”