Polynomial Anonymous Dynamic Distributed Computing without a Unique Leader

TL;DR

This paper investigates the problem of counting nodes in anonymous dynamic networks without relying on a unique leader, exploring the minimal information needed and presenting new results for such scenarios.

Contribution

It introduces the first analysis of counting in anonymous dynamic networks without a single distinguished node, addressing both positive and negative results.

Findings

Established bounds on counting without a leader

Identified minimal information requirements for counting

Provided algorithms and impossibility results

Abstract

Counting the number of nodes in Anonymous Dynamic Networks is enticing from an algorithmic perspective: an important computation in a restricted platform with promising applications. Starting with Michail, Chatzigiannakis, and Spirakis [19], a flurry of papers sped up the running time guarantees from doubly-exponential to polynomial [16]. There is a common theme across all those works: a distinguished node is assumed to be present, because Counting cannot be solved deterministically without at least one. In the present work we study challenging questions that naturally follow: how to efficiently count with more than one distinguished node, or how to count without any distinguished node. More importantly, what is the minimal information needed about these distinguished nodes and what is the best we can aim for (count precision, stochastic guarantees, etc.) without any. We present negative and positive results to answer these questions. To the best of our knowledge, this is the first work that addresses them.