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Unknotted Strand Routings of Triangulated Meshes

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DNA Computing and Molecular Programming (DNA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10467))

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Abstract

In molecular self-assembly such as DNA origami, a circular strand’s topological routing determines the feasibility of a design to assemble to a target. In this regard, the Chinese-postman DNA scaffold routings of Benson et al. (2015) only ensure the unknottedness of the scaffold strand for triangulated topological spheres. In this paper, we present a cubic-time \(\frac{5}{3}-\)approximation algorithm to compute unknotted Chinese-postman scaffold routings on triangulated orientable surfaces of higher genus. Our algorithm guarantees every edge is routed at most twice, hence permitting low-packed designs suitable for physiological conditions.

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Notes

  1. 1.

    By convention, if \(k=0\), then \(v_0\) is affinely independent.

  2. 2.

    Detachments are also defined in the literature [11] for multigraphs without an associated embedding.

  3. 3.

    \(X^{\star }\) is the subgraph of the dual of M induced by the duals of the cut edges.

  4. 4.

    Although stated only for Eulerian multigraphs embedded on a plane, Tsai and West’s proof also holds for Eulerian multigraphs embedded on any surface since the resplicing occurs locally at vertices.

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Authors and Affiliations

  1. Aalto University, Espoo, Finland

    Abdulmelik Mohammed

  2. University of South Florida, Tampa, FL, USA

    Mustafa Hajij

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  1. Abdulmelik Mohammed
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  2. Mustafa Hajij
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Correspondence to Abdulmelik Mohammed .

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Editors and Affiliations

  1. Hasselt University, Diepenbeek, Belgium

    Robert Brijder

  2. California Institute of Technology, Pasadena, California, USA

    Lulu Qian

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Mohammed, A., Hajij, M. (2017). Unknotted Strand Routings of Triangulated Meshes. In: Brijder, R., Qian, L. (eds) DNA Computing and Molecular Programming. DNA 2017. Lecture Notes in Computer Science(), vol 10467. Springer, Cham. https://doi.org/10.1007/978-3-319-66799-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-66799-7_4

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