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Algorithmic Tile Self-Assembly Model for the Minimum Set Cover Problem

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Abstract:

The study of algorithmic tile self-assembly model shows the development of self-assembling systems for solving complex computational problems. This computation model is considered as a promising technique in nanotechnology. The minimum set cover problem is a classical NP-complete problem in computer science. In this paper, the algorithmic tile self-assembly model is used to implement the minimum set cover problem by executing four operations: nondeterministic guess operation, AND operation, copy operation and the comparing operation. This method can be successfully performed the minimum set cover problem in Θ(mn) steps. Here, m is the number of the elements of the set X for the given minimum set cover problem, and n is the number of a family of subsets of X.

Keywords: ALGORITHMIC; MINIMUM SET COVER PROBLEM; SELF-ASSEMBLY; TILE

Document Type: Research Article

DOI: http://dx.doi.org/10.1166/jbns.2012.1079

Publication date: December 1, 2012

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  • Bionanoscience attempts to harness various functions of biological macromolecules and integrate them with engineering for technological applications. It is based on a bottom-up approach and encompasses structural biology, biomacromolecular engineering, material science, and engineering, extending the horizon of material science. The journal aims at publication of (i) Letters (ii) Reviews (3) Concepts (4) Rapid communications (5) Research papers (6) Book reviews (7) Conference announcements in the interface between chemistry, physics, biology, material science, and technology. The use of biological macromolecules as sensors, biomaterials, information storage devices, biomolecular arrays, molecular machines is significantly increasing. The traditional disciplines of chemistry, physics, and biology are overlapping and coalescing with nanoscale science and technology. Currently research in this area is scattered in different journals and this journal seeks to bring them under a single umbrella to ensure highest quality peer-reviewed research for rapid dissemination in areas that are in the forefront of science and technology which is witnessing phenomenal and accelerated growth.
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