Fair Allocation with Interval Scheduling Constraints

TL;DR

This paper investigates fair scheduling of interval jobs on heterogeneous machines, ensuring fairness criteria like maximin share and envy-freeness, and provides approximation algorithms for these complex constraints.

Contribution

It introduces approximation algorithms for fair resource allocation with interval scheduling constraints under maximin share and envy-freeness criteria.

Findings

Existence of fair allocations varies with problem settings.

Constant approximation algorithms are developed for both fairness criteria.

The algorithms effectively handle heterogeneity and scheduling constraints.

Abstract

We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by agents. Each job is associated with release time, deadline, and processing time such that it can be processed if its complete processing period is between its release time and deadline. The machines gain possibly different utilities by processing different jobs, and all jobs assigned to the same machine should be processed without overlap. We consider two widely studied solution concepts, namely, maximin share fairness and envy-freeness. For both criteria, we discuss the extent to which fair allocations exist and present constant approximation algorithms for various settings.