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

TL;DR

This paper analyzes the energy-latency tradeoff in in-network function computation within random networks, proposing policies that achieve near-optimal energy efficiency under latency constraints, considering various network topologies and function types.

Contribution

It introduces a policy for in-network computation that is order-optimal in energy consumption under latency constraints for random networks, extending to general functions and different network models.

Findings

Proposed policy achieves order-optimal energy consumption.

Energy scaling depends on path-loss exponent and network dimension.

Extended policy applies to general functions with certain latency limits.

Abstract

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.