A macro-level model for investigating the effect of directional bias on network coverage

TL;DR

This paper develops a macro-level Markov chain model to analyze how directional bias in random walks affects network coverage times, revealing that bias can significantly improve efficiency under certain conditions.

Contribution

It introduces a novel macro-level model for biased random walks on networks, enabling efficient analysis of coverage times based on bias and network size.

Findings

Directional bias reduces coverage time when below a certain threshold.

The optimal bias depends on network size.

Bias beyond the threshold does not improve coverage efficiency.

Abstract

Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random walks that are biased towards their current heading. In this paper, we investigate whether or not complementing random walks with directional bias can decrease the expected discovery and coverage times in networks. To do so, we develop a macro-level model of a directionally biased random walk based on Markov chains. By focussing on regular, connected networks, the model allows us to efficiently calculate expected coverage times for different network sizes and biases. Our analysis shows that directional bias can significantly reduce coverage time, but only when the bias is below a certain value which is dependent on the network size.