Gathering an even number of robots in an odd ring without global multiplicity detection

TL;DR

This paper introduces a protocol for gathering an even number of anonymous, oblivious robots in an odd ring network using only local weak multiplicity detection, achieving convergence under specific conditions.

Contribution

The paper presents a novel gathering protocol that works with symmetric initial configurations and local detection, extending previous work to more general conditions.

Findings

Works with symmetric but not periodic initial configurations

Achieves gathering in O(n^2) asynchronous rounds

Requires more than 8 robots and an odd ring with specific size constraints

Abstract

We propose a gathering protocol for an even number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non- atomic CORDA model with asynchronous fair scheduling. In our scheme, the number of robots k must be greater than 8, the number of nodes n on a network must be odd and greater than k+3. The running time of our protocol is O(n2) asynchronous rounds.