Broadcast in radio networks: time vs. energy tradeoffs

TL;DR

This paper investigates the tradeoffs between time and energy efficiency in broadcast algorithms for wireless radio networks, proposing new randomized algorithms that optimize energy use while maintaining near-optimal broadcast times.

Contribution

It introduces two novel randomized algorithms that balance energy consumption and broadcast time in unknown multi-hop radio networks, with proven near-optimality under certain conditions.

Findings

Algorithms achieve near-optimal broadcast time with low energy per station.

Proposed algorithms work for graphs with arbitrary diameter and unknown topology.

Lower bounds establish the limits of energy efficiency for given time constraints.

Abstract

In wireless networks, consisting of battery-powered devices, energy is a costly resource and most of it is spent on transmitting and receiving messages. Broadcast is a problem where a message needs to be transmitted from one node to all other nodes of the network. We study algorithms that can work under limited energy measured as the maximum number of transmissions by a single station. The goal of the paper is to study tradeoffs between time and energy complexity of broadcast problem in multi-hop radio networks. We consider a model where the topology of the network is unknown and if two neighbors of a station are transmitting in the same discrete time slot, then the signals collide and the receiver cannot distinguish the collided signals from silence. We observe that existing, time efficient, algorithms are not optimized with respect to energy expenditure. We then propose and analyse two new randomized energy-efficient algorithms. Our first algorithm works in time $O((D+\varphi)\cdot n^{1/\varphi}\cdot \varphi)$ with high probability and uses $O(\varphi)$ energy per station for any $\varphi \leq \log n/(2\log\log n)$ for any graph with $n$ nodes and diameter $D$. Our second algorithm works in time $O((D+\log n)\log n)$ with high probability and uses $O(\log n/\log\log n)$ energy. We prove that our algorithms are almost time-optimal for given energy limits for graphs with constant diameters by constructing lower bound on time of $\Omega(n^{1/\varphi} \cdot \varphi)$. The lower bound shows also that any algorithm working in polylogaritmic time in $n$ for all graphs needs energy $\Omega(\log n/\log\log n)$.