Energy-Efficient Maximal Independent Sets in Radio Networks
Dominick Banasik, Varsha Dani, Fabien Dufoulon, Aayush Gupta, Thomas P. Hayes, Gopal Pandurangan
TL;DR
The paper tackles MIS in energy-constrained radio networks with unknown topology, introducing energy-focused randomized MIS algorithms for both CD and no-CD models. It develops a Luby-inspired, bitwise competition framework in CD achieving $O( ext{log } n)$ energy and $O( ext{log }^2 n)$ rounds, and proves a matching lower bound of $oldsymbol{Ω( ext{log } n)}$ energy. In the more challenging no-CD setting, it presents an algorithm with $O( ext{log }^2 n ext{log log } n)$ energy and $O( ext{log }^3 n ext{log } Δ)$ rounds, using energy-aware backoffs and a subroutine on low-degree subgraphs to bridge the gap to optimal round complexities. Overall, the work significantly advances energy-efficient distributed MIS in arbitrary radio-topologies, offering both tight lower bounds and near-optimal algorithms with practical implications for battery-powered wireless networks.
Abstract
The maximal independent set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the Radio Network model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm, which we want to minimize. We present new, more energy-efficient MIS algorithms in radio networks with arbitrary and unknown graph topology. We present algorithms for two popular variants of the radio model -- with collision detection (CD) and without collision detection (no-CD). Specifically, we obtain the following results: 1. CD model: We present a randomized distributed MIS algorithm with energy complexity $O(\log n)$, round complexity $O(\log^2 n)$, and failure probability $1 / poly(n)$, where $n$ is the network size. We show that our energy complexity is optimal by showing a matching $Ω(\log n)$ lower bound. 2. no-CD model: In the more challenging no-CD model, we present a randomized distributed MIS algorithm with energy complexity $O(\log^2n \log \log n)$, round complexity $O(\log^3 n \log Δ)$, and failure probability $1 / poly(n)$. The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of $O(\log^3 n)$ of the best known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.