Accelerating Amoebots via Reconfigurable Circuits

TL;DR

This paper introduces reconfigurable circuits in the amoebot model, enabling faster algorithms for leader election, consensus, shape recognition, and other problems in programmable matter.

Contribution

It extends the amoebot model with circuits, allowing for significantly improved algorithmic efficiency in distributed shape and consensus tasks.

Findings

Leader election in Θ(log n) rounds, w.h.p.

Consensus achieved in O(1) rounds.

Shape recognition within Θ(log n) or O(1) rounds, w.h.p.

Abstract

We consider an extension to the geometric amoebot model that allows amoebots to form so-called \emph{circuits}. Given a connected amoebot structure, a circuit is a subgraph formed by the amoebots that permits the instant transmission of signals. We show that such an extension allows for significantly faster solutions to a variety of problems related to programmable matter. More specifically, we provide algorithms for leader election, consensus, compass alignment, chirality agreement and shape recognition. Leader election can be solved in $\Theta(\log n)$ rounds, w.h.p., consensus in $O(1)$ rounds and both, compass alignment and chirality agreement, can be solved in $O(\log n)$ rounds, w.h.p. For shape recognition, the amoebots have to decide whether the amoebot structure forms a particular shape. We show how the amoebots can detect a parallelogram with linear and polynomial side ratio within $\Theta(\log{n})$ rounds, w.h.p. Finally, we show that the amoebots can detect a shape composed of triangles within $O(1)$ rounds, w.h.p.