Efficient Parallel Self-Assembly Under Uniform Control Inputs

TL;DR

This paper demonstrates that using uniform control inputs, complex micro-scale shapes can be assembled in sublinear or even constant time, significantly improving efficiency over traditional sequential methods in programmable matter.

Contribution

It introduces a novel staged assembly model with uniform external forces, enabling sublinear and constant construction times for large-scale micro-objects, advancing self-assembly theory.

Findings

Sublinear construction times for a wide class of shapes.

Constant time assembly for convex polyominoes.

Pipelining approach achieves amortized constant production time.

Abstract

We prove that by successively combining subassemblies, we can achieve sublinear construction times for "staged" assembly of micro-scale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield micro-factories.The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number N of particles, which is inefficient for large N. Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time.