Graph AlgorithmsCptS 223

Getting from here to there...

What data structure would you use ?

A

B

C

D

E F

G

H

How do you even think about the

problem ?

Lets strip away the the irrelevant details..

Getting from here to there...

Vertices

A

B

C

D

E F

G

H

A

B

C

D

E F

G

H

Edges

Getting from here to there...

5

7

10

48

6

3

5

A

B

C

D

E F

G

H

Weights

Getting from here to there...

looks a lot more simpler now...

5

7

10

48

6

3

5

A

B

C

D

E F

G

H

Getting from here to there...

Graphs

• Are a tool for modeling real world problems.

• Allow us to abstract details and focus on the problem.

• We can represent our domain as graphs apply algorithms to solve our problem.

Simple Graphs

G = (V,E)

(u, v) ∈ E

u

v

Directed Graphs

(u, v) ∈ E

u

v

(v, u) !∈ E

Weighted Graphs

5

7

10

48

6

3

5

Path Cycle

Representation of graphs

A

B

C

A

B

C

A

B

C

B A

C

0 1 1

1 0 1

1 1 0

A

B

C

A B C

Adjacency Matrix Adjacency List

|V 2| |V | + |E|

Use Adjacency lists

forSparse Graphs

Topological Sort

A

B

C

D

E

F

G

H

A,B,D,C,E,F,G,H

A

C

B

No Cycles

Topological Sort

In degree = 3

Out degree = 1

Topological Sort

A

B

C

D

E

F

G

H

A,B,D,C,E,F,G,HO(|V |2)

Topological Sort

A

B

C

D

E

F

G

H

A,B,D,C,E,F,G,H

O(|V | + |E|)