[176926] |

Title: Graph-based Methods for the Design of DNA Computations. |

Written by: Svetlana Torgasin |

in: January (2012). |

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Series: 20120115-phdthesis-torgasin.pdf |

Address: Hamburg / Germany |

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ISBN: 10.15480/882.1049 |

how published: 12-95 Torgasin12 PhD |

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School: Hamburg University of Technology |

Institution: School of Electrical Engineering, Computer Science and Mathematics |

Type: Ph.D. Thesis. |

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**Note: **AEG

**Abstract: **The reliability of results in DNA based computations strongly depends on the DNA sequences representing the units of information. The task of finding appropriate sequences is currently handled by means of conventional computing. The most accurate criterium for this purpose is the free energy of hybridization complexes built by two DNA single strands. This thesis addresses two issues in this area. First, finding of a secondary structure of DNA/DNA complexes having minimal free energy. For this, a novel graph-based representation of DNA/DNA complexes is introduced and two advanced methods calculating the free energy based on dynamic programming are proposed. Second, the validation of a given set of DNA words to encode a particular assignment of a mathematical problem. For this, a method is developed based on free energy assessment. It is suitable for DNA computing models that are based on an interdependent encoding of DNA words, which represent two different types of entities in the mathematical problem. Another accomplishment of the thesis is an optimization of the Floyd-Warshall algorithm for finding shortest paths in a weighted graph. A memory reduction method for the particular case of bipartite graphs is established.