B.
FILTERING MODELS
231
B
Filtering models
¶
1.
Filtering models:
Operate by filtering out of the solution molecules
that are not part of the solution.
¶
2. A solution can be treated mathematically as a finite
bag
or
multiset
of
molecules,
and filtering operations can be treated as operations to produce multi
sets from multisets.
¶
3.
Initial multiset:
Typically, for a problem of size
n
, strings of size
O
(
n
) are required.
Should contain enough strings to include many copies all possible so
lutions.
Therefore, for an exponential problem, we will have
O
(
k
n
) strings.
¶
4. This is essentially a bruteforce method.
B.1
Adleman: HPP
B.1.a
Review of HPP
¶
1.
Hamiltonian Path Problem (HPP):
The
Hamiltonian Path Prob
lem
is to determine, for a given directed graph
G
= (
V, E
) and two of
its vertices
v
in
, v
out
2
V
, whether there is a HP from
v
in
to
v
out
, that
is, a path that goes through each vertex exactly once.
¶
2.
NPcomplete:
HPP is an NPcomplete problem.
¶
3. We will see that for Adleman’s algorithm the
number of algorithm steps
is linear in problem size.
¶
4.
Laboratory demonstration:
Leonard Adleman gave a laboratory
demonstration of the procedure in 1994 (for
n
= 7).
(By the way, he is the “A” of “RSA.”)
¶
5. “In 2002, he and his research group managed to solve a ‘nontriv
ial’ problem using DNA computation.
Specifically, they solved a 20
variable SAT problem having more than 1 million potential solutions.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
232
CHAPTER IV.
MOLECULAR COMPUTATION
7
1
2
3
4
5
6
Figure IV.6: HPP solved by Adleman. The HP is indicated by the dotted
edges. [source: Amos, Fig. 5.2]
They did it in a manner similar to the one Adleman used in his seminal
1994 paper.”
4
B.1.b
Problem Representation
¶
1. The heart of Adleman’s algorithm is a clever way to encode candidate
paths in DNA.
¶
2.
Vertices:
Vertices were represented by singlestranded 20mers, that
is, sequences of 20nt (nucleotides).
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '13
 BruceMacLennan
 DNA, Hamiltonian path problem, Adleman, Leonard Adleman

Click to edit the document details