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.Comment: 15 page