Optimally Gathering Two Robots

TL;DR

This paper introduces an optimal algorithm for gathering two robots in a non-rigid asynchronous setting, using minimal communication via two-color lights and distance measurement, overcoming previous impossibility results.

Contribution

It presents the first deterministic gathering algorithm for two robots with only two-color lights and distance measurement in the non-rigid ASYNC model.

Findings

Successful gathering in finite time under the given model.

Optimal use of two colors for lights, matching the minimal possible.

Overcomes previous impossibility results for single-color lights.

Abstract

We present an algorithm that ensures in finite time the gathering of two robots in the non-rigid ASYNC model. To circumvent established impossibility results, we assume robots are equipped with 2-colors lights and are able to measure distances between one another. Aside from its light, a robot has no memory of its past actions, and its protocol is deterministic. Since, in the same model, gathering is impossible when lights have a single color, our solution is optimal with respect to the number of used colors.