Brief Announcement: Energy-Efficient Maximal Independent Sets in Radio Networks

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 networks 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.We present the first 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 distributed MIS algorithm with O (log n) energy complexity (n is the network size). We also show a matching ω (log n) lower bound for the energy complexity.(2) no-CD model: In the more challenging no-CD model, we present a distributed MIS algorithm with energy complexity O (log2 n log log n). The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of O (log3 n) of the best-known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.