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# colorcode - Color Coding Speeding up Network Searches 858L...

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Color Coding Speeding up Network Searches 858L

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Efficient Algorithms for Detecting Signaling Pathways in Protein Interaction Networks Scott, Ideker, Karp, Sharan RECOMB 2005 Color Coding: Alon et al, 1995.
Searching for High Scoring Paths v u p(u,v) = probability this edge exists w(u,v) = - log p(u,v) Weighted network G: P = simple path Weight(P) = sum of w(u,v) values along its edges Length(P) = number of nodes in P G might be an alignment graph, a PPI network, metabolic network, etc...

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{ } I = v Goal: Low-weight, simple, length-k paths G = P Given : Graph G, a subset of nodes I, and a node v . Find : The lowest-weight path P that: (1) starts at some vertex in I (2) ends at v (3) is of length k and is simple (doesn’t use any vertex twice) Set I let’s us specify, e.g., that the path should start at a surface receptor protein.
Is this Problem Hard? Given : Graph G, a subset of nodes I, and a node v . Find: The lowest-weight , simple , length- k path between I and v.

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Is this Problem Hard? Given : Graph G, a subset of nodes I, and a node v . Find: The lowest-weight , simple , length- k path between I and v. Yes. It’s NP-hard. Why?
Is this Problem Hard? Given : Graph G, a subset of nodes I, and a node v . Find: The lowest-weight , simple , length- k path between I and v. Yes. It’s NP-hard. Why? Reduce Hamiltonian Cycle (HC) to it: To solve an HC instance <G H >, let G = G H , I = { v }, and k = n .

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Is this Problem Hard? Given : Graph G, a subset of nodes I, and a node v .
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colorcode - Color Coding Speeding up Network Searches 858L...

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