Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms

TL;DR

This paper studies the minimum-energy broadcast problem in random-grid ad-hoc networks, providing lower bounds, approximation algorithms, and a distributed protocol with near-optimal energy efficiency and balanced load.

Contribution

It introduces a lower bound, an approximation algorithm, and a distributed protocol for energy-efficient broadcasting in non-uniform random-grid networks.

Findings

Lower bound of (1-ε) n/π on energy cost

Approximation algorithm with energy cost ≤ 1.1204 n/π

Distributed protocol with energy cost ≤ 8n and O(log n) time

Abstract

The Min Energy broadcast problem consists in assigning transmission ranges to the nodes of an ad-hoc network in order to guarantee a directed spanning tree from a given source node and, at the same time, to minimize the energy consumption (i.e. the energy cost) yielded by the range assignment. Min energy broadcast is known to be NP-hard. We consider random-grid networks where nodes are chosen independently at random from the $n$ points of a $\sqrt n \times \sqrt n$ square grid in the plane. The probability of the existence of a node at a given point of the grid does depend on that point, that is, the probability distribution can be non-uniform. By using information-theoretic arguments, we prove a lower bound $(1-\epsilon) \frac n{\pi}$ on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than $1.1204 \frac n{\pi}$. Finally, we present a fully-distributed protocol that constructs a broadcast range assignment of energy cost not larger than $8n$,thus still yielding constant approximation. The energy load is well balanced and, at the same time, the work complexity (i.e. the energy due to all message transmissions of the protocol) is asymptotically optimal. The completion time of the protocol is only an $O(\log n)$ factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least $1-1/n^{\Theta(1)}$.