Paper by Erik D. Demaine

Reference:
Erik D. Demaine, Matthew J. Patitz, Robert T. Schweller, and Scott M. Summers, “Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor”, in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011), Dortmund, Germany, March 10–12, 2011, pages 201–212.

Abstract:
We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling.

Comments:
The full paper is available as arXiv.org:1004.4383 of the Computing Research Repository (CoRR).

Copyright:
Copyright held by the authors. Licensed under the Creative Commons Attribution-No Derivative Works 3.0 license.

Availability:
The paper is available in PDF (671k).
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Last updated June 22, 2017 by Erik Demaine.