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arXiv · 1807.01584

Efficient Parallel Self-Assembly Under Uniform Control Inputs

Arne Schmidt·Sheryl Manzoor·Li Huang·Aaron T. Becker·Sándor P. Fekete
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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.

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Arne Schmidt, Sheryl Manzoor, Li Huang, Aaron T. Becker, Sándor P. Fekete. 2018-07-04. Efficient Parallel Self-Assembly Under Uniform Control Inputs. https://arxiv.org/abs/1807.01584

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