Given a set of real numbers output a sequence l 1 l i l n where l i l i 1 for i 1 n1 Naive Algorithm For index i 1 ID: 694616
Download Presentation The PPT/PDF document "Preliminaries–Computational Problem" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1Slide2
Preliminaries–Computational Problem
Given a set of real numbers, output a sequence,
(
l
1
, … ,
l
i
, … ,
l
n
)
,
where
l
i
≤
l
i+1
for
i
=
1 … n-1 .
Naive Algorithm
For index
i
=1 ..
n-1,
if
l
i
>
l
i
+1
then
swap
the two numbers.
Repeat until a complete pass for
i
=
1
…
n-1
is made without making any swaps.
Any better algorithms?Slide3
Point of the Exercise
Computational Problem is abstract
Decouples the application entirely from solving the problem.
Helps communicate the problem in a universal and understandable language
another
algorithmist
may find a solution (either by coming up with one, or noticing the problem is similar to a formulation used in another discipline)
http://www.sorting-algorithms.com/Slide4
Protein Complex Formation
Motivation
Experiments have shown numerous proteins that bind or aggregate together.
Identify protein complexes?
Problem Formulation
Inputs?
Get a list of proteins and the partners they bind to.
Objectives?
Find the protein with the most partners and form an initial complex. Keep adding proteins if they bind to all members of the group.
Output?
The collection of proteins in the complex.
Plausible Algorithm?
NOT POSSIBLE!?!?!Slide5
The Computational Biology ProcessSlide6
Computational Problem Formulation
Given a graph G(V,E), output all
maximal
cliques of size at least
k
.
A clique C is a set of vertices that form a complete
subgraph
.
Maximal
clique C’ is a clique where the addition of any vertex v in V\C’ does not form a clique.
Problems
Tractability?
O(3
n/3
)
Adequate?
Choosing parameter
k?
Every clique in a Protein-Protein Interaction network is not a protein complex.
Two proteins do not bind, but may still form a complex.
Wang et al. 2010
– Recent Paper on Cluster/Module/Complex Identification in PPI