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We consider distributed algorithms for data aggregation and functioncomputation in sensor networks. The algorithms perform pairwise computationsalong edges of an underlying communication graph. A token is associated witheach sensor node, which acts as a transmission permit. Nodes with active tokenshave transmission permits; they generate messages at a constant rate and sendeach message to a randomly selected neighbor. By using different strategies tocontrol the transmission permits we can obtain tradeoffs between message andtime complexity. Gossip corresponds to the case when all nodes have permits allthe time. We study algorithms where permits are revoked after transmission andrestored upon reception. Examples of such algorithms include Simple-RandomWalk(SRW), Coalescent-Random-Walk(CRW) and Controlled Flooding(CFLD) and theirhybrid variants. SRW has a single node permit, which is passed on in thenetwork. CRW, initially initially has a permit for each node but these permitsare revoked gradually. The final result for SRW and CRW resides at a single(orfew) random node(s) making a direct comparison with GOSSIP difficult. A hybridtwo-phase algorithm switching from CRW to CFLD at a suitable pre-determinedtime can be employed to achieve consensus. We show that such hybrid variantsachieve significant gains in both message and time complexity. The per-nodemessage complexity for n-node graphs, such as 2D mesh, torii, and Randomgeometric graphs, scales as $O(polylog(n))$ and the corresponding timecomplexity scales as O(n). The reduced per-node message complexity leads toreduced energy utilization in sensor networks.

A Token Based Algorithm to Distributed Computation in Sensor Networks