Line-Recovery by Programmable Particles

TL;DR

This paper presents a fault-tolerant method for programmable particles to recover a line shape after some particles crash, regardless of initial conditions and under semi-synchronous activation.

Contribution

It introduces a novel line recovery algorithm for anonymous, programmable particles that tolerates crashes and works under semi-synchronous scheduling.

Findings

Recovers line shape despite up to n-5 crashes.

Works with arbitrary initial distributions and orientations.

Operates under semi-synchronous activation conditions.

Abstract

Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line shape, used as a tool for the construction of more complex configurations. We present a solution to the line recovery problem by the non-faulty anonymous particles; the solution works regardless of the initial distribution and number $f<n-4$ of faults, of the local orientations of the non-faulty entities, and of the number of non-faulty entities activated in each round (i.e., semi-synchronous adversarial scheduler).