On distributed computation of information potentials

A common task of mobile wireless ad-hoc networks is to distributedly extract information from a monitored process. We deńe process information as a measure that is sensed and computed by each mobile node in a network. For complex tasks, such as searching in a network and coordination of robotic swarms, we are typically interested in the spatial distribution of the process information. Spatial distributions can be thought of as information potentials that recursively consider the richness of information around each node. This paper describes a localized mechanism for determining the information potential on each node based on local process information and the potential of neighboring nodes. The mechanism allows us to distributedly generate a spectrum of possible information potentials between the extreme points of a local view and distributed averaging. In this work, we describe the mechanism, prove its exponential convergence, and characterize the spectrum of information potentials. Moreover, we use the mechanism to generate information potentials that are unimodal, i.e., feature a single extremum. Unimodality is a very valuable property for chemotactic search, which can be used in diverse application tasks such as directed search of information and rendezvous of mobile agents.