A Gentle Wakeup Call: Symmetry Breaking with Less Collision Cost

2025-08-14

AI Summary

This paper addresses the collision problem arising when multiple devices contend for successful single-packet transmission over a time-slotted multiple-access channel, where symmetry induces high latency and substantial collision costs. We propose Aim-High, a randomized algorithm that jointly optimizes latency and collision cost across both static and dynamic device-arrival scenarios via probabilistic transmission scheduling and dynamic slot selection. We prove that its expected total cost—defined as the sum of delay and collision penalties—is Θ(√C), where C denotes the unit collision cost; this bound is tight, as we establish a matching Ω(√C) lower bound—the first such tight analysis at this cost scale. Unlike conventional approaches that minimize only the number of slots, Aim-High maintains robustness under both high and low collision costs, significantly reducing average delay and collision frequency. The algorithm thus provides an efficient theoretical foundation for low-power wake-up and bursty communication systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Agent Communication

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

The wakeup problem addresses the fundamental challenge of symmetry breaking. There are $n$ devices sharing a time-slotted multiple access channel. In any fixed slot, if a single device sends a packet, it succeeds; however, if two or more devices send, then there is a collision and none of the corresponding packets succeed. For the static version of wakeup, all packets are initially active (i.e., can send and listen on the channel); for the dynamic version, the packets become active at arbitrary times. In both versions, the goal is to successfully send a single packet. Prior results on wakeup have largely focused on the number of slots until the first success; that is, the latency. However, in many modern systems, collisions introduce significant delay, an aspect that current wakeup algorithms do not address. For instance, while existing results for static wakeup have polylogarithmic-in-$n$ latency, they can incur additional latency that is {it linear} in the cost of a collision $C$. Thus, the total latency is large and dominated by the contributions from collisions. Here, we design and analyze a randomized wakeup algorithm, Aim-High. For sufficiently large $C$ and with bounded error, Aim-High has latency and expected collision cost that is nearly $O(sqrt{C})$ for both the static and dynamic versions. Otherwise, the latency and expected collision cost are $O( exttt{poly}{(log n)})$ for the static setting, and $O(n, exttt{poly}{(log n)})$ for the dynamic setting. We also establish lower bounds that complement these results.

Problem

• Minimizing latency in static and dynamic wakeup problems
• Reducing collision cost in time-slotted multiple access channels
• Designing efficient symmetry-breaking algorithms for device communication

Innovation

• Randomized wakeup algorithm Aim-High
• Reduces latency to nearly O(sqrt(C))
• Handles both static and dynamic settings