Prior-Independent Mechanisms for Scheduling

TL;DR

This paper introduces prior-independent truthful mechanisms for scheduling on unrelated selfish machines, achieving constant and sublogarithmic approximations to expected makespan without needing distributional knowledge.

Contribution

It presents the first prior-independent truthful mechanisms for makespan minimization that do not rely on job size distribution knowledge.

Findings

Mechanisms achieve constant approximation ratios under certain distributional assumptions.

Mechanisms achieve sublogarithmic approximation ratios in general settings.

No truthful anonymous deterministic mechanism can provide sublinear approximation in prior-free settings.

Abstract

We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under various distributional assumptions provide constant and sublogarithmic approximations to expected makespan. Our mechanisms are prior-independent in that they do not rely on knowledge of the job size distributions. Prior-independent approximation mechanisms have been previously studied for the objective of revenue maximization [Dhangwatnotai, Roughgarden and Yan'10, Devanur, Hartline, Karlin and Nguyen'11, Roughgarden, Talgam-Cohen and Yan'12]. In contrast to our results, in prior-free settings no truthful anonymous deterministic mechanism for the makespan objective can provide a sublinear approximation [Ashlagi, Dobzinski and Lavi'09].