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Author:Mohammed, Abdulmelik
Title:Combinatorial algorithms for the design of nanoscale systems
Publication type:Master's thesis
Publication year:2014
Pages:72      Language:   eng
Department/School:Perustieteiden korkeakoulu
Main subject:Tietojenkäsittelyteoria   (T-79)
Supervisor:Orponen, Pekka
Instructor:Czeizler, Eugen
Electronic version URL: http://urn.fi/URN:NBN:fi:aalto-201507013655
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto     | Archive
Keywords:DNA nanotechnology
DNA origami
polyhedra
graphs
combinatorial algorithms
Abstract (eng): Over the past 30 years, DNA, with its exquisitely specific Watson-Crick base pairing rules, has found a novel use as a nanoscale construction material in DNA nanotechnology.
DNA origami is a popular recent technique in DNA nanotechnology for the design and synthesis of DNA nanoscale shapes and patterns.
DNA origami operates by the folding of a single long strand of DNA called a scaffold with the help of numerous shorter strands of DNA called staples.
Recently, DNA origami design for polyhedral beam-frameworks has been proposed where a scaffold strand is conceptually routed over the beams of a polyhedron so that complementary strands potentially fold the scaffold to the framework in a solution.

In this work, we modelled the problem of finding a scaffold routing path for polyhedral frameworks in graph-theoretic terms whereby the routing path was found to coincide with a specific type of Eulerian trail, called an A-trail, on the polyhedral skeleton.
We studied the complexity of deciding whether an A-trail exists with an emphasis on rigid triangular frameworks or equivalently on plane triangulations.
While the decision problem was found to be NP-complete in general, we learned that Eulerian triangulations always have A-trails if a long standing conjecture by Barnette on the Hamiltonicity of bipartite cubic polyhedral graphs holds.

Given the general NP-completeness result, we developed a backtracking search algorithm for finding A-trails.
To improve the backtrack search; we introduced an enumeration heuristic, tuned in particular to Eulerian triangulations, to schedule the nodes in the search tree.
The algorithm, guided by the heuristic, efficiently found A-trails for a family of Eulerian triangulations as well as a family of braced grid graphs.
Furthermore, we implemented a software package, BScOR (Beam Scaffolded-Origami Routing), which generates an A-trail, or equivalently a scaffold routing path, given a three-dimensional object description in a Polygon File Format.
ED:2014-03-03
INSSI record number: 48706
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