An Early-Stopping Protocol for Computing Aggregate Functions in Sensor Networks

Abstract

In this paper, we study algebraic aggregate computations in Sensor Networks. The main contribution is the presentation of an early-stopping protocol that computes the average function under a harsh model of the conditions under which sensor nodes operate. This protocol is shown to be time-optimal in presence of unfrequent failures. The approach followed saves time and energy by relying the computation on a small network of delegate nodes that can be rebuilt fast in case of node failures and communicate using a collisionfree schedule. Delegate nodes run simultaneously two protocols, namely, a collection/dissemination tree-based algorithm, which is shown to be optimal, and a mass-distribution algorithm. Both algorithms are analyzed under a model where the frequency of failures is a parameter. Other aggregate computation algorithms can be easily derived from this protocol. To the best of our knowledge, this is the first optimal early-stopping algorithm for aggregate computations in Sensor Networks.

Fault-Tolerant Aggregation: Flow-Updating Meets Mass-Distribution

“…We focus on the algorithmic cost of such computation, counting only the number of rounds that the computation takes after simultaneous startup of all nodes, leaving aside medium access issues to other layers. This assumption could be removed as in [10].…”

“…Previous work on aggregate computations has been particularly prolific for the area of Radio Networks, including both theoretical and experimental work [8, 12-16, 19, 20, 22-24, 26, 35]. Many of those and other aggregation techniques exploit global information of the network [10,12,22,23], or are not resilient to message loss [3,5,19].…”

“…As in previous work [3,6,10,19], MDFU is based on repeatedly sharing among neighbors a fraction of the average estimated so far. Unlike in those papers, in MDFU the estimation is computed from scratch in each round, as in FU [17,18].…”

“…A classic distributed technique for aggregation, sometimes called Mass-Distribution (MD) [10], works in rounds. In each round, each node shares a fraction of its current average estimation with other nodes, starting from the input values [3,5,6,19,27,29,32,33].…”