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# Ch9MsmithNote - Chapter 9 Computational Molecular Biology...

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Chapter 9 – Computational Molecular Biology Michael Smith Introduction This chapter discusses how molecular biology is used to solve hard algorithmic problems DNA computing has the ultimate aim of creating very efficient biomolecular computers 9.1 The Hamiltonian Path Problem This section discusses how to solve the Hamiltonian path problem in directed graphs (HDPP) with DNA molecules The DNA molecules are used in a laboratory method which comprises of a series of procedures which grow linearly with the number of vertices in the graph The Hamiltonian path problem is NP-complete The heart of this DNA method is a brute force algorithm executing an exponential number of operations which are executed in parallel, thereby enabling the method to have a linear number of laboratory procedures The problem to be solved is : given a directed graph G=(V,E) such that |V|=n and |E|=m and two distinguished vertices s and t , verify whether the graph has a path (s,v 1 ,v 2 ,….,t) whose length is n-1 and whose vertices are all distinct; figure 9.1 A brute force algorithm involves generating all possible paths with n-1 edges and verify whether one of them obeys the constraints of the problem There are at most (n-2)! Paths A modified version of the brute force algorithm involves generating a large number of random path, instead of all paths Random path generation has the possibility of generating independent paths, thus they can be created simultaneously The complete algorithm is (1) generate random paths, (2) keep only those path

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Ch9MsmithNote - Chapter 9 Computational Molecular Biology...

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