Maximal dispersion of adaptive random walks

TL;DR

This paper introduces an adaptive random walk that maximizes network dispersion by updating transition rules based on local information, overcoming the global knowledge requirement of maximum entropy random walks.

Contribution

It proposes a novel adaptive random walk method derived from large-deviation principles, enabling efficient dispersion without global network knowledge.

Findings

ARW effectively maximizes dispersion in various networks

ARW outperforms traditional methods in local information scenarios

Theoretical derivation links ARW to MERW via large deviations

Abstract

Maximum entropy random walks (MERWs) are maximally dispersing and play a key role in optimizing information spreading in various contexts. However, building MERWs comes at the cost of knowing beforehand the global structure of the network, a requirement that makes them totally inadequate in real case scenarios. Here, we propose an adaptive random walk (ARW), which instead maximizes dispersion by updating its transition rule on the local information collected while exploring the network. We show how to derive ARW via a large-deviation representation of MERW and study its dynamics on synthetic and real world networks.