The Fair Periodic Assignment Problem

TL;DR

This paper introduces efficient algorithms for the fair periodic assignment problem, balancing efficiency and fairness in task scheduling, and demonstrates that fairness can be achieved with minimal additional resources.

Contribution

It formalizes fairness in periodic task assignment, analyzes the efficiency-fairness trade-off, and provides optimal algorithms for fair scheduling.

Findings

The price of fairness is at most one extra worker.

A fair solution can be found using the Nearest Neighbor heuristic.

Allowing aperiodic schedules does not reduce the price of fairness.

Abstract

We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a O(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always be found using the Nearest Neighbor heuristic. We characterize all instances that admit a solution that is both fair and efficient, and use this result to develop a O(n log n) exact algorithm for the fair periodic assignment problem. Finally, we show that allowing aperiodic schedules never reduces the price of fairness.