Energy-Latency Tradeoff for In-Network Function Computation in Random Networks

The problem of designing policies for in-network function computation with minimum energy consumption subject to a latency constraint is considered. The scaling behavior of the energy consumption under the latency constraint is analyzed for random networks, where the nodes are uniformly placed in growing regions and the number of nodes goes to infinity. The special case of sum function computation and its delivery to a designated root node is considered first. A policy which achieves order-optimal average energy consumption in random networks subject to the given latency constraint is proposed. The scaling behavior of the optimal energy consumption depends on the path-loss exponent of wireless transmissions and the dimension of the Euclidean region where the nodes are placed. The policy is then extended to computation of a general class of functions which decompose according to maximal cliques of a proximity graph such as the $k$-nearest neighbor graph or the geometric random graph. The modified policy achieves order-optimal energy consumption albeit for a limited range of latency constraints.Comment: A shorter version appears in Proc. of IEEE INFOCOM 201

Minimum Cost Data Aggregation with Localized Processing for Statistical Inference

The problem of minimum cost in-network fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center performs an optimal statistical-inference test on the correlated measurements, drawn from a Markov random field. Conditioned on the delivery of a sufficient statistic for inference to the fusion center, the structure of optimal routing and fusion is shown to be a Steiner tree on a transformed graph. This Steiner-tree reduction preserves the approximation ratio, which implies that any Steinertree heuristic can be employed for minimum cost fusion with the same approximation ratio. The proposed fusion scheme involves routing packets of two types viz., raw measurements sent for local processing, and aggregates obtained on combining these processed values. The performance of heuristics for minimum cost fusion are evaluated through theory and simulations, showing a significant saving in routing costs, when compared to routing all the raw measurements to the fusion center. Index Terms — Sensor networks, in-network processing and aggregation, statistical inference, cost minimization I