Silent Self-Stabilising Leader Election in Programmable Matter Systems with Holes

TL;DR

This paper introduces the first self-stabilising leader election algorithm for programmable matter systems with holes, enabling unique leader election in connected configurations using particle movement and shared orientation.

Contribution

It presents a novel self-stabilising leader election algorithm for connected programmable matter systems that employs particle movement and shared orientation, overcoming classical impossibility results.

Findings

First self-stabilising leader election algorithm for systems with holes.

Algorithm guarantees leader election under unfair scheduling.

Utilizes particle movement to achieve self-stabilisation.

Abstract

Leader election is a fundamental problem in distributed computing, particularly within programmable matter systems, where coordination among simple computational entities is crucial for solving complex tasks. In these systems, particles (i.e., constant-memory computational entities) operate in a regular triangular grid as described in the geometric Amoebot model. While leader election has been extensively studied in non self-stabilising settings, self-stabilising solutions remain more limited. In this work, we study the problem of self-stabilising leader election in connected (but not necessarily simply connected) configurations. We present the first self-stabilising algorithm for connected programmable matter systems that guarantees the election of a unique leader under an unfair scheduler, for oblivious particles (i.e., particles with no persistent memory) that share a common sense of direction. Our approach leverages particle movement, a capability not previously exploited in the self-stabilising context. We show that movement in conjunction with particles sharing a sense of orientation and operating in a grid can overcome classical impossibility results for constant-memory systems established by Dolev, Gouda and Schneider (1999).