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

2025-07-27

AI Summary

This work addresses the self-stabilizing leader election problem in connected programmable matter configurations containing arbitrary holes. Under constraints of no global identifiers, constant-memory particles, and no centralized control, it is the first to circumvent classical impossibility results for leader election under unfair schedulers by leveraging particle mobility—assuming shared directional sense. Based on the geometric Amoebot model, we design a distributed self-stabilizing algorithm wherein local state-update rules drive convergence while jointly coordinating grid structure maintenance and particle motion. Our algorithm guarantees that, from any arbitrary initial configuration (including those with holes), the system always converges to a unique-leader stable state. This constitutes the first self-stabilizing leader election protocol supporting arbitrary hole-containing configurations in programmable matter, thereby establishing a foundational primitive for distributed coordination in such systems.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Deterministic Planning
• Multiagent Systems: Distributed Problem Solving

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 programmable matter that guarantees the election of a unique leader under an unfair scheduler, assuming particles 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 operating in a grid can overcome classical impossibility results for constant-memory systems established by Dolev et al.

Problem

• Self-stabilising leader election in programmable matter systems
• Overcoming impossibility results with particle movement
• Ensuring unique leader under unfair scheduler

Innovation

• Self-stabilising leader election algorithm
• Uses particle movement in grid
• Overcomes constant-memory impossibility results