Graph Reductions and its Application in Parallel Gene Assembly

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Azadi, Mohammad | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43467 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahmoodian, Ebadollah
Abstract:
In the process of gene assembling, the molecular structure of a DNA chain, can be modeled by a signed graph. After that by means of a composition of three reduction rules: gnr, gpr and gdr, that is called reduction strategy, this graph is reduced to a null graph. If the composition of any ordering of rules in a reduction strategy such as S, is applicable on a signed graph G, then we say that S can be applied in parallel to G and the set S is said to be a parallel step for reduction of that graph. Also we define the least number of parallel steps in reduction of a graph, to be the parallel complexity of that graph, and denote it C(G). In this thesis, a collection of particular signed graphs, such as: complete graphs, cycles, bipartite graphs and trees, we investigate the reduction strategies, parallel complexity, upper bound for parallel complexity, conditions for parallelism of reduction rules and so on. Also we state some open problems.
Keywords:
Parallelism ; Graph Reduction ; Parallel Complexity ; Gene Assembly