Robust and Optimal Contention Resolution without Collision Detection

BSTRACTContention resolution on a multiple-access communication channel is a classical problem in distributed and parallel computing. In this problem, a set of nodes arrive over time, each with a message it intends to send. Time proceeds in synchronous slots, and in each slot each node can broadcast its message or remain idle. If in a slot one node broadcasts alone, it succeeds; otherwise, if multiple nodes broadcast simultaneously, messages collide and none succeeds. Nodes can differentiate collision and silence (that is, no node broadcasts) only if a collision detection mechanism is available. Ideally, a contention resolution algorithm should satisfy at least three criteria: (a) low time complexity (i.e., high throughput), meaning it does not take too long for all nodes to succeed; (b) low energy complexity, meaning each node does not make too many broadcast attempts before it succeeds; and (c) strong robustness, meaning the algorithm can maintain good performance even if interference is present. Such interference is often modeled by jamming---a jammed slot always generates collision. 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 "perfect" contention resolution algorithms? In other words, when collision detection is absent and jamming is present, can we achieve both low total time complexity and low per-node energy cost? In this paper, we answer the above question affirmatively. Specifically, a new randomized algorithm for robust contention resolution is developed, assuming collision detection is not available. Lower bound results demonstrate it achieves both optimal time complexity and optimal energy complexity. If all nodes start execution simultaneously---which is often referred to as the "static case" in literature---another algorithm is developed that runs even faster. The separation on time complexity suggests, for robust contention resolution without collision detection, "batch" instances (that is, nodes start simultaneously) are inherently easier than "scattered" ones (that is, nodes arrive over time).