Energy-Efficient Maximal Independent Sets in Radio Networks

2025-10-09

AI Summary

This paper addresses the energy-efficient distributed construction of a maximal independent set (MIS) in wireless broadcast networks, aiming to minimize the number of wake-up rounds per node to reduce energy consumption. We consider two classic radio network models—those with and without collision detection—under a power-saving model where nodes can enter sleep mode. Our approach introduces novel randomized algorithms grounded in probabilistic analysis. In the collision-detection model, we achieve the first optimal energy complexity of $O(log n)$ and round complexity of $O(log^2 n)$, accompanied by matching lower bounds. In the no-collision-detection model, we significantly improve the state-of-the-art energy complexity from $O(log^3 n)$ to $O(log^2 n cdot log log n)$. All results strictly dominate prior work, providing both theoretical foundations and practical algorithmic guarantees for low-power wireless ad hoc networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

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.

Problem

• Designing energy-efficient MIS algorithms for radio networks
• Optimizing energy consumption in wireless ad hoc networks
• Developing distributed algorithms with minimal awake rounds

Innovation

• Energy-efficient MIS algorithm with collision detection
• Optimal O(log n) energy complexity for CD model
• Improved O(log²n log log n) energy for no-CD model