Graph-based heuristics for rest difference minimisation
针对锦标赛中队伍间休息时间差异导致的不公平问题，提出了基于图论的启发式算法来最小化休息差异，其中一种方法显著优于已有结果，并分析了经典赛程表的性质。
Complaints often arise from teams with less rest time between games in a tournament, highlighting the importance of minimising rest differences for fairness. Achieving fairness through rest difference minimisation is an empirically hard problem when determining the opponents and matchdays of teams in a tournament. To address this issue, we propose novel heuristic approaches based on graph theory. Remarkably, one of our heuristic methods significantly outperforms previously reported outcomes. We also show that the widely used canonical schedule has the maximum optimal rest difference value among all possible opponent schedules, and if the number of rounds is a prime number, shuffling the rounds within the canonical schedule offers no advantages in reducing rest differences. Furthermore, we present an efficient integer programming formulation to determine the total rest difference for a given opponent schedule.