# A Novel Graph-Based Heuristic Approach for Solving Sport Scheduling Problem

• Meriem Khelifa
• Dalila Boughaci
• Esma Aïmeur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)

## Abstract

This paper proposes an original and effective heuristic approach for solving the unconstrained traveling tournament problem (denoted by UTTP) in sport scheduling. UTTP is an interesting variant of the well-known NP-hard traveling tournament problem (TTP) where the main objective is to find a tournament schedule that minimizes the total distances traveled by the teams. The proposed graph-based heuristic method starts with a set of n teams $$(n< 10)$$. The method models the problem by representing the home locations of the teams as vertices and each arc corresponds to the matching between two teams. Each round corresponds to a 1-factor of the generated graph. We use the Bron-Kerbosch clique detection algorithm to enumerate all the possible $$2(n-1)$$ cliques from the 1-factors. Then, the vertices of each $$2(n-1)$$ cliques are sorted to create double round robin tournament (DRRT) schedules. The schedule with lowest cost travel is selected to be the solution of the problem. The proposed method is evaluated on several instances and compared with the state-of-the-art. The numerical results are promising and show the benefits of our method. The proposed method significantly improves the current best solutions for the US National Baseball League (NL) instances and produces new good solutions for the Rugby League (SUPER) instances.

## Keywords

Sport scheduling Traveling tournament problem Heuristic Perfect matching Graph Unconstrained traveling tournament problem

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