We consider in-network processing via local message passing. The considered setting involves a set of sensors each of which can communicate with a subset of other sensors. There is no designated fusion center; instead sensors exchange messages on the associated communication graph to obtain a global estimate. We propose an asynchronous distributed algorithm based on local fusion between neighboring sensors. The algorithm differs from other related schemes such as gossip algorithms in that after each local fusion one of the associated sensors ceases its activity until it is re-activated by reception of messages from a neighboring sensor. This leads to substantial gains in energy expenditure over existing local ad-hoc messaging algorithms such as gossip and belief propagation algorithms. Our results are general and we focus on some explicit graphs, namely geometric random graphs, which have been successfully used to model wireless networks, and d-dimensional lattice torus with n nodes, which behave exactly like mesh networks as n gets large. We quantify the time, message and energy scaling of the algorithm, where the analysis is built upon the coalescing random walks. In particular, for the planar torus the completion time of the algorithm is Θ(n log n) and energy requirement per sensor node is O((log n)2) and for 3-d torus these quantities are Θ(n) and O(log n) respectively. The energy requirement of the algorithm is thus scalable, and interestingly there appears little practical incentive to consider higher dimensions. Furthermore, for the planar torus the algorithm exhibits a very favorable tradeoff relative to gossip algorithms whose time and energy requirements are shown here to be Ω(n). Also, the proposed algorithm can be generalized to robustify against packet losses and permanent node failures without entailing significant energy overhead. The paper concludes with numerical results.
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