Download Preliminaries * Computational Problem

PRELIMINARIES–COMPUTATIONAL PROBLEM
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Given a set of real numbers, output a sequence,
(l1 , … , li , … , ln), where li ≤ li+1 for i = 1 … n-1 .
Naive Algorithm
For index i=1 .. n-1, if li > li+1 then swap the two
numbers.
 Repeat until a complete pass for i = 1 … n-1 is made
without making any swaps.
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Any better algorithms?
POINT OF THE EXERCISE
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Computational Problem is abstract
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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/
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PROTEIN COMPLEX FORMATION
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Motivation
Experiments have shown numerous proteins that bind
or aggregate together.
 Identify protein complexes?
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Problem Formulation
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Inputs?
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Objectives?
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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?
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Get a list of proteins and the partners they bind to.
The collection of proteins in the complex.
Plausible Algorithm?
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NOT POSSIBLE!?!?!
THE COMPUTATIONAL BIOLOGY PROCESS
Biological
Motivation
Computational
Problem Formulation
Tractability?
Adequate?
YES
YES
Proceed to Design
an efficient
ALGORITHM
COMPUTATIONAL PROBLEM FORMULATION
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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.
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Problems
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Tractability?
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O(3n/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.
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Wang et al. 2010 – Recent Paper on
Cluster/Module/Complex Identification in PPI