Copula-based Randomized Mechanisms for Truthful Scheduling on Two Unrelated Machines

TL;DR

This paper introduces a novel copula-based randomized truthful mechanism for scheduling on two unrelated machines, achieving improved approximation bounds and demonstrating the potential of copula techniques in mechanism design.

Contribution

It presents a new copula-based approach for truthful scheduling mechanisms, providing tighter bounds and explicit incorporation of copula concepts in the analysis.

Findings

Approximation ratio within [1.5852, 1.58606] for two-machine scheduling.

Upper bound of 1.5067711 for two-machine two-task case.

Copula techniques offer promising tools for mechanism design.

Abstract

We design a Copula-based generic randomized truthful mechanism for scheduling on two unrelated machines with approximation ratio within $[1.5852, 1.58606]$, offering an improved upper bound for the two-machine case. Moreover, we provide an upper bound 1.5067711 for the two-machine two-task case, which is almost tight in view of the lower bound of 1.506 for the scale-free truthful mechanisms [4]. Of independent interest is the explicit incorporation of the concept of Copula in the design and analysis of the proposed approximation algorithm. We hope that techniques like this one will also prove useful in solving other problems in the future.