An Improved Randomized Truthful Mechanism for Scheduling Unrelated Machines

TL;DR

This paper presents an improved randomized truthful mechanism for scheduling on unrelated machines, achieving better approximation ratios than previous methods and extending results to multiple machines.

Contribution

It introduces a new mechanism that improves the approximation ratio for two machines and generalizes to multiple machines, surpassing prior bounds.

Findings

Achieves a 1.6737-approximation for two machines.

Provides a $0.8368m$-approximation for m machines.

Improves previous upper bounds on approximation ratios.

Abstract

We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper (Nisan and Ronen 1999), where they gave a 1.75-approximation randomized truthful mechanism for the case of two machines. We improve this result by a 1.6737-approximation randomized truthful mechanism. We also generalize our result to a $0.8368m$-approximation mechanism for task scheduling with $m$ machines, which improve the previous best upper bound of $0.875m(Mu'alem and Schapira 2007).