Equilibration through local information exchange in networks

TL;DR

This paper investigates equilibrium states of energy functions on network links, using advanced methods, and develops a distributed algorithm for resource allocation that aligns with theoretical predictions.

Contribution

It introduces a novel approach combining cavity and replica methods to analyze energy equilibria and proposes an efficient distributed algorithm for network resource allocation.

Findings

Theoretical analysis matches simulation results.

Scaling laws relate network connectivity to resource distribution.

Distributed algorithm achieves optimal resource allocation.

Abstract

We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.