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 NPcomplete
•
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
n1
and whose vertices are all distinct; figure 9.1
•
A brute force algorithm involves generating all possible paths with n1 edges and
verify whether one of them obeys the constraints of the problem
•
There are at most
(n2)!
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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 Fall '11
 Mitra
 DNA, Test Tube, brute force algorithm, Hamiltonian path problem, random path generation

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