Scheduling Asynchronous Round-Robin Tournaments

TL;DR

This paper analyzes scheduling methods for asynchronous round-robin tournaments, comparing their fairness and quality, and proposes an optimal schedule for odd numbers of teams.

Contribution

It identifies limitations of the circle design for odd teams and introduces a new schedule that optimally addresses all measures of fairness and quality.

Findings

Circle design performs well for even teams

Circle design is suboptimal for odd teams

Proposed schedule is optimal for odd teams

Abstract

We study the problem of scheduling asynchronous round-robin tournaments. We consider three measures of a schedule that concern the quality and fairness of a tournament. We show that the schedule generated by the well-known "circle design" performs well with respect to all three measures when the number of teams is even, but not when the number of teams is odd. We propose a different schedule that performs optimally with respect to all measures when the number of teams is odd.