On the Nisan-Ronen conjecture

TL;DR

This paper advances the understanding of the Nisan-Ronen conjecture by establishing a new lower bound of 1+sqrt(n-1) for the approximation ratio of truthful mechanisms in makespan minimization on unrelated machines.

Contribution

It provides a significant new lower bound for the conjecture, moving closer to the conjectured ratio of n, thus deepening theoretical insights into mechanism design limitations.

Findings

New lower bound of 1+sqrt(n-1) for truthful mechanisms

Progress towards validating the Nisan-Ronen conjecture

Enhanced understanding of approximation limits in mechanism design

Abstract

The Nisan-Ronen conjecture states that no truthful mechanism for makespan-minimization when allocating $m$ tasks to $n$ unrelated machines can have approximation ratio less than $n$. Over more than two decades since its formulation, little progress has been made in resolving it and the best known lower bound is still a small constant. This work makes progress towards validating the conjecture by showing a lower bound of $1+\sqrt{n-1}$.