Wake Up and Join Me! An Energy-Efficient Algorithm for Maximal Matching in Radio Networks

TL;DR

This paper introduces an energy-efficient distributed randomized algorithm for finding a maximal matching in wireless radio networks, achieving low energy costs and latency, and also proposes a neighbor backup assignment with minimized load.

Contribution

The paper presents a novel distributed randomized algorithm for maximal matching with provably optimal energy and time bounds, and a low-energy neighbor backup assignment method.

Findings

Maximum energy cost per node is O(log^2 n).

Total algorithm latency is O(n log n) time steps.

Neighbor backup assignment has a maximum load within polylog(n) of optimal.

Abstract

We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is $O(\log^2 n)$, where $n$ is the size of the network. The total latency of our algorithm is $O(n \log n)$ time steps. We observe that there exist families of network topologies for which both of these bounds are simultaneously optimal up to polylog factors, so any significant improvement will require additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present a decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog($n$) factor bigger that the optimum.