A quest for a fair schedule: The Young Physicists' Tournament

TL;DR

This paper addresses scheduling fairness in the Young Physicists' Tournament by formalizing conditions, proposing graph-based solutions, and developing integer linear programming models tested on real and synthetic data.

Contribution

It formalizes fairness conditions for tournament scheduling, models them using bipartite graph edge colorings, and introduces ILP methods to generate fair schedules.

Findings

Fair schedules can be ensured by bipartite graph edge colorings.

Integer linear programming effectively finds feasible schedules.

Models perform well on real and synthetic data.

Abstract

The Young Physicists Tournament is an established team-oriented scientific competition between high school students from 37 countries on 5 continents. The competition consists of scientific discussions called Fights. Three or four teams participate in each Fight, each of whom presents a problem while rotating the roles of Presenter, Opponent, Reviewer, and Observer among them. The rules of a few countries require that each team announce in advance 3 problems they will present at the national tournament. The task of the organizers is to choose the composition of Fights in such a way that each team presents each of its chosen problems exactly once and within a single Fight no problem is presented more than once. Besides formalizing these feasibility conditions, in this paper we formulate several additional fairness conditions for tournament schedules. We show that the fulfillment of some of them can be ensured by constructing suitable edge colorings in bipartite graphs. To find fair schedules, we propose integer linear programs and test them on real as well as randomly generated data.