Energy-Constrained Programmable Matter Under Unfair Adversaries

TL;DR

This paper introduces a framework that enables energy-constrained programmable matter modules to run existing algorithms with minimal overhead, even under unfair adversaries, by transforming energy-agnostic algorithms into energy-aware ones.

Contribution

The authors present a general energy distribution framework for amoebot programmable matter that preserves algorithm behavior and extends applicability to energy-constrained, asynchronous settings.

Findings

Framework transforms energy-agnostic algorithms with $ ext{O}(n^2)$ overhead.

Existing algorithms for leader election and shape formation are compatible with the framework.

Simulations demonstrate effective energy-constrained algorithm performance.

Abstract

Individual modules of programmable matter participate in their system's collective behavior by expending energy to perform actions. However, not all modules may have access to the external energy source powering the system, necessitating a local and distributed strategy for supplying energy to modules. In this work, we present a general energy distribution framework for the canonical amoebot model of programmable matter that transforms energy-agnostic algorithms into energy-constrained ones with equivalent behavior and an $\mathcal{O}(n^2)$-round runtime overhead -- even under an unfair adversary -- provided the original algorithms satisfy certain conventions. We then prove that existing amoebot algorithms for leader election (ICDCN 2023) and shape formation (Distributed Computing, 2023) are compatible with this framework and show simulations of their energy-constrained counterparts, demonstrating how other unfair algorithms can be generalized to the energy-constrained setting with relatively little effort. Finally, we show that our energy distribution framework can be composed with the concurrency control framework for amoebot algorithms (Distributed Computing, 2023), allowing algorithm designers to focus on the simpler energy-agnostic, sequential setting but gain the general applicability of energy-constrained, asynchronous correctness.