Designing Local Distributed Mechanisms

TL;DR

This paper introduces local mechanisms that combine truthful distributed algorithms with approximation guarantees for graph problems, establishing a new link between distributed algorithms and mechanism design.

Contribution

It presents a novel framework for designing local, truthful mechanisms from monotone distributed algorithms, applied to fundamental graph problems.

Findings

Monotone distributed algorithms can be transformed into truthful mechanisms.

Critical prices can be computed with the same complexity as the original algorithms.

The approach extends distributed mechanism design to local resource allocation problems.

Abstract

In this work we introduce a new notion: local mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and non-trivial approximation guarantees. We show how monotone distributed optimisation algorithms can be turned into truthful mechanisms using Myerson's Lemma. We demonstrate mechanisms for four fundamental graph problems: maximum-weight independent set, minimum-weight vertex cover, minimum-weight dominating set, and a variant of weighted colouring. We show how these mechanisms can be implemented in the distributed setting. The key observation is that computing the so-called critical prices of a monotone algorithm can be done with the same time complexity as the original algorithm in the LOCAL model of distributed computing. Our work establishes a new connection between algorithmic mechanism design and distributed graph algorithms. We pose several open questions, such as can critical prices be computed with small messages. It also points to the importance of designing monotone distributed optimisation algorithms. Our work extends previous work in Distributed Algorithmic Mechanism Design (DAMD) in a new direction. Instead of studying global problems like routing or leader election, we study local resource allocation problems. Our algorithms are simple and thus potentially practical. Local algorithms are particularly interesting for highly dynamic large-scale systems, and there are many potential future application domains, e.g. demand-side load management in electric grids or resource allocation in IoT computing.