A Gentle Wakeup Call: Symmetry Breaking with Less Collision Cost

TL;DR

This paper introduces Aim-High, a randomized algorithm for the wakeup problem that optimizes latency and collision costs, especially when collision delay C is large, improving efficiency over prior methods.

Contribution

The paper presents Aim-High, a novel randomized wakeup algorithm that reduces collision costs and latency, adapting to different collision delay regimes, and analyzes a trade-off between latency and collision costs.

Findings

Aim-High achieves nearly O(√C) expected latency when C is large.

When C is small, Aim-High attains O(polylog n) latency.

Established a trade-off between latency and collision cost for a class of algorithms.

Abstract

The wakeup problem addresses the fundamental challenge of symmetry breaking. Initially, n devices share a time-slotted multiple access channel, which models wireless communication. A transmission succeeds if exactly one device sends in a slot; if two or more transmit, a collision occurs and none succeed. The goal is to achieve a single successful transmission efficiently. Prior work on wakeup primarily analyzes latency -- the number of slots until the first success. However, in many modern systems, each collision incurs a nontrivial delay, C, which prior analyses neglect. Consequently, although existing algorithms achieve polylogarithmic-in-n latency, they still suffer a delay of \Omega(C) due to collisions. Here, we design and analyze a randomized wakeup algorithm, Aim-High. When C is sufficiently large with respect to n, Aim-High has expected latency and expected total cost of collisions that are nearly O(\sqrt{C}); otherwise, both quantities are O(poly{\log n}). Finally, for a well-studied class of algorithms, we establish a trade-off between latency and expected total cost of collisions.