An efficient algorithm for detecting frequent subgraphs in biological networks

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An efficient algorithm for detecting frequent
subgraphs in biological networks
Class presentation for CPSC 689-604

• Authors Mehmet Kouturk, Ananth Grama and
• Wojciech Szpankowski
• Presented by Songjian Lu
• Professor Jianer Chen

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Contents

• Introduction
• Metabolic Pathways in detail
• Mining metabolic pathways
• Algorithm
• Result
• Some comments

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Introduction-1

• Metabolic pathways
• Model to a directed graph
• Noderepresenting enzymes
• Edgerepresenting the product of one enzyme is
  consumed by a reaction catalyzed by another enzyme

enzyme
enzyme
enzyme
enzyme
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Introduction-2

• Protein interaction network
• Noderepresenting Protein
• Edgerepresenting interaction between proteins
• Pairwise interactionsgetting by two-hybrid
  experiments
• Multi-way interactionsgetting by mass
  spectrometry experiments
• Database BIND(http//www.blueprint.org/bind)
• Database DIP(http//dip.doe-mbi.ucla.edu/)

protein
protein
protein
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Metabolic pathway detail-1

• DEFINITIONA metabolic pathway P(M,Z,R) is a
  collection of metabolites M, enzymes Z, and
  reactions R, where each reaction r?R is
  associated with a set of enzymes Z(r)?Z, a set of
  substrates S(r)?M, and a set of products T(r) ?M.

Z(r)
T(r)
S(r)
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Metabolic pathway detail-2

• DEFINITIONGiven metabolic pathway P(M,Z,R), the
  associated directed graph G(V,E) of P is
  constructed as followsfor any enzyme zi ? Z,
  there is a node vi ? V. There is an edge from vi
  to vj, i.e. (vi,vj) ? E if and only if ?r1,r2 ?
  R, such that zi ? Z(r1), zj ? Z(r2) and
  T(r1)?S(r2) ? ?.

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Metabolic pathway detail-3
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Mining Metabolic pathways-1

• DEFINITIONGiven a collection of graphs
  G1,G2,,Gn and support threshold ?, the Maximal
  Frequent Subgraph Discovery problem is one of
  finding all maximal connected subgraphs that are
  contained in at least ?n of the input graphs.

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Mining Metabolic pathways-2
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Algorithm
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Result-1
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Result-2
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Comment-1

• Graph isomorphism problem is very hard
• Given two graphs, if they are isomorphic?
• Given two graphs, if one graph is isomorphic to a
  subgraph of another graph?

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Comment-2

• Given two graph G1, G2, if there exists a induced
  subgraph of k vertices in G1 and a induced
  subgraph of k vertices in G2, such that these two
  subgraph are isomorphic?(w1 hard)
• Given two graph G1, G2, if there exists a
  subgraph of k edges in G1 and a subgraph of k
  edges in G2, such that these two subgraphs are
  isomorphic?(w1 hard)
• Given two graph G1, G2, if there exists a subtree
  of k vertices in G1 and a subtree of k vertices
  in G2, such that these two subtrees are
  isomorphic?(FPT)
• Given two graph G1, G2, if there exists a subpath
  of k vertices in G1 and a subpath of k vertices
  in G2, such that these two subpaths are
  isomorphic?(FPT)

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Comment-3

• Given two graph G1, G2, if there exists a induced
  subgraph of k vertices in G1 and a induced
  subgraph of k vertices in G2, such that these two
  subgraph are isomorphic?(w1 hard)

G1
G2
G
v1
v1
v1
v1
v1
v1
v1
v1
v1
v1
v1
v1
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Thank you very much
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Homework

• Problem 1 Given G1(V1,E1),G2(V2,E2), and
  integer k, if there exists a subgraph G1 of k
  edges in G1, a subgraph G2 of k edges in G2 such
  that there is an isomorphic mapping ? from G1 to
  G2. Prove this problem is NP-complete.
• Problem2Given G(V,E), I?V, and integer k, if
  there exists a subtree T of k vertices, such that
  all leaves are in I. Prove this problem is
  NP-complete.