Self-stabilizing Determinsitic Gathering

TL;DR

This paper presents a deterministic self-stabilizing algorithm for the gathering problem in weak robots, showing it works if and only if the number of robots is odd, leveraging strong multiplicity detection.

Contribution

It introduces the concept of strong multiplicity detection and proves its necessity and sufficiency for deterministic gathering with odd number of robots.

Findings

Deterministic gathering is possible with strong multiplicity detection for odd n.

Gathering cannot be deterministically achieved for even n under the same conditions.

The algorithm is self-stabilizing, ensuring robustness to initial configurations.

Abstract

In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, deaf and dumb, and oblivious). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a deterministic self-stabilizing algorithm solving GP for n robots if, and only if, n is odd.