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Preliminaries–Computational Problem

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.

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Preliminaries–Computational Problem

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  1. Preliminaries–Computational Problem • Given a set of real numbers, output a sequence, (l1 , … , li , … , ln), where li≤ li+1for 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. • Any better algorithms?

  2. 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/

  3. 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!?!?!

  4. The Computational Biology Process

  5. 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(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. • Wang et al. 2010 – Recent Paper on Cluster/Module/Complex Identification in PPI

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