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Preliminaries–Computational Problem Preliminaries–Computational Problem

Preliminaries–Computational Problem - PowerPoint Presentation

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Preliminaries–Computational Problem - PPT Presentation

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

protein problem clique complex problem protein complex clique proteins form bind computational formulation output find algorithms maximal complete numbers algorithm partners set

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Slide1
Slide2

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