2. P RELIMINARIES –C OMPUTATIONAL P ROBLEM 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?

3. P OINT OF THE E XERCISE 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/

4. P ROTEIN C OMPLEX F ORMATION 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!?!?!

5. T HE C OMPUTATIONAL B IOLOGY P ROCESS Biological Motivation Computational Problem Formulation Tractability?Adequate? YES Proceed to Design an efficient ALGORITHM

6. C OMPUTATIONAL P ROBLEM F ORMULATION 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. 2010Wang et al. 2010 – Recent Paper on Cluster/Module/Complex Identification in PPI