Energy-Efficient Aggregation and Minimum-Degree Spanning Trees in Radio Networks

2026-05-28

AI Summary

This work addresses the problem of energy-efficient global aggregation (e.g., summation) in synchronous multi-hop radio networks without collision detection, where each message is limited to $O(\log n)$ bits. The authors propose a randomized distributed algorithm that unifies, for the first time, the construction of an approximately optimal maximum-degree spanning tree with low-energy aggregation scheduling. With high probability, the algorithm completes aggregation within $O(n \operatorname{polylog} n)$ rounds while ensuring that each node’s energy cost—measured as the number of active rounds—is $O(\Delta^* \operatorname{polylog} n)$, where $\Delta^*$ denotes the minimum possible maximum degree of any spanning tree of the network graph. The constructed spanning tree has maximum degree within an $O(\log n)$ factor of $\Delta^*$, and both endpoints of every tree edge learn their membership. The energy complexity nearly matches the theoretical lower bound.

Abstract

We study the aggregation problem in synchronous multi-hop radio networks with $O(\log n)$-bit messages and no collision detection. Each node initially holds a value, and the goal is to compute a global aggregate such as the sum of all values. Aggregation tasks arise naturally in wireless sensor networks, where nodes are often battery-powered and radio activity is the dominant source of energy consumption. Accordingly, our main objective is to minimize the energy complexity, defined as the maximum number of rounds in which any node is awake. Our main result is a randomized distributed algorithm that, with high probability, constructs and executes an aggregation schedule in $O(n \operatorname{polylog} n)$ rounds and using $O(Δ^\ast \operatorname{polylog} n)$ energy, where $Δ^\ast$ is the minimum possible maximum degree of a spanning tree of the network graph. This guarantee is nearly optimal: for any aggregation schedule and any graph, there exists a node that must be awake for at least $Δ^\ast$ rounds. As a by-product, the algorithm also computes a spanning tree whose maximum degree is within an $O(\log n)$ factor of $Δ^\ast$, with the same round and energy guarantees. For every tree edge, both endpoints learn that the edge belongs to the tree.

Problem

• energy-efficient aggregation
• radio networks
• minimum-degree spanning trees
• energy complexity
• distributed algorithms

Innovation

• energy complexity
• aggregation
• minimum-degree spanning tree
• radio networks
• distributed algorithm