Introduction to Bioinformatics

Biological Networks

Department of ComputingImperial College London

Spring 2010

Nataša Pržuljnatasha@imperial.ac.uk

2

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Nataša Pržuljnatasha@imperial.ac.uk

- Pseudocode (Chpt 1.1)- Growth Rate of Running Time

by Goodrich and Tamassia

Graph Algorithms Review Continued

3

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Nataša Pržuljnatasha@imperial.ac.uk

4

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Nataša Pržuljnatasha@imperial.ac.uk

However: beware of large constants!

55

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Nataša Pržuljnatasha@imperial.ac.uk

66

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Nataša Pržuljnatasha@imperial.ac.uk

77

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Nataša Pržuljnatasha@imperial.ac.uk

888

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

9

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

10

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

1111

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

1212

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Nataša Pržuljnatasha@imperial.ac.uk

Applications of DFS:(DFS is O(|V| + |E|), i.e., linear time)• path finding• cycle finding• topological sort (ordering of vertices of G such that uv is in E implies that u appears before v in the ordering)• Strongly Connected Components (SCCs) of a digraph• A digraph is strongly connected if every vertex is reachable from every other vertex following the directions of the arcs (edges)

13

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(follows from definitions)

1414

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Nataša Pržuljnatasha@imperial.ac.uk

In digraphs searches must follow the directions of edges.

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Nataša Pržuljnatasha@imperial.ac.uk

1616

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Nataša Pržuljnatasha@imperial.ac.uk

1717

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

1818

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Nataša Pržuljnatasha@imperial.ac.uk

1919

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2020

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

2121

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2222

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142, 202)

2323

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Nataša Pržuljnatasha@imperial.ac.uk

2424

Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2525

Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2626

Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2727

Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2828

Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

2929

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

30

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

3131

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

3232

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

3333

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 142)

3434

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

3535

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

36

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

3737

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

3838

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

3939

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

4040

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

4141

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

4242

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Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

43

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

44

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

45

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)

46

Assumed Knowledge of Graph Theory and Algorithms:

Nataša Pržuljnatasha@imperial.ac.uk

(Review: Computing 202)