Robust and Optimal Contention Resolution without Collision Detection

TL;DR

This paper introduces a new randomized algorithm for contention resolution without collision detection that achieves optimal time and energy efficiency, addressing a long-standing open problem in distributed computing.

Contribution

It presents the first robust contention resolution algorithm without collision detection that attains both optimal time and low energy complexity, including specialized algorithms for simultaneous node start.

Findings

Achieves optimal time complexity without collision detection.

Ensures low energy cost per node.

Shows faster algorithms for simultaneous start scenarios.

Abstract

We consider the classical contention resolution problem where nodes arrive over time, each with a message to send. In each synchronous slot, each node can send or remain idle. If in a slot one node sends alone, it succeeds; otherwise, if multiple nodes send simultaneously, messages collide and none succeeds. Nodes can differentiate collision and silence only if collision detection is available. Ideally, a contention resolution algorithm should satisfy three criteria: low time complexity (or high throughput); low energy complexity, meaning each node does not make too many broadcast attempts; strong robustness, meaning the algorithm can maintain good performance even if slots can be jammed. Previous work has shown, with collision detection, there are "perfect" contention resolution algorithms satisfying all three criteria. On the other hand, without collision detection, it was not until 2020 that an algorithm was discovered which can achieve optimal time complexity and low energy cost, assuming there is no jamming. More recently, the trade-off between throughput and robustness was studied. However, an intriguing and important question remains unknown: without collision detection, are there robust algorithms achieving both low total time complexity and low per-node energy cost? In this paper, we answer the above question affirmatively. Specifically, we develop a new randomized algorithm for robust contention resolution without collision detection. Lower bounds show that it has both optimal time and energy complexity. If all nodes start execution simultaneously, we design another algorithm that is even faster, with similar energy complexity as the first algorithm. The separation on time complexity suggests for robust contention resolution without collision detection, ``batch'' instances (nodes start simultaneously) are inherently easier than ``scattered'' ones (nodes arrive over time).