Sublinear-time Collision Detection with a Polynomial Number of States in Population Protocols

TL;DR

This paper introduces a novel population protocol algorithm that detects collisions efficiently with polynomial states per agent, achieving sublinear parallel time with high probability, addressing a key open problem in distributed computing.

Contribution

It presents the first polynomial-state, sublinear-time collision detection algorithm in population protocols, solving an open problem from prior research.

Findings

Achieves collision detection in sublinear parallel time

Uses a polynomial number of states per agent

Works with high probability and in expectation

Abstract

This paper addresses the collision detection problem in population protocols. The network consists of state machines called agents. At each time step, exactly one pair of agents is chosen uniformly at random to have an interaction, changing the states of the two agents. The collision detection problem involves each agent starting with an input integer between $1$ and $n$, where $n$ is the number of agents, and requires those agents to determine whether there are any duplicate input values among all agents. Specifically, the goal is for all agents to output false if all input values are distinct, and true otherwise. In this paper, we present an algorithm that requires a polynomial number of states per agent and solves the collision detection problem with probability one in sub-linear parallel time, both with high probability and in expectation. To the best of our knowledge, this algorithm is the first to solve the collision detection problem using a polynomial number of states within sublinear parallel time, affirmatively answering the question raised by Burman, Chen, Chen, Doty, Nowak, Severson, and Xu [PODC 2021] for the first time.