Prepare for your exams
Get points
Guidelines and tips
Sell on Docsity
Docsity AI

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Docsity AI

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Connected Components in Graph Theory - Prof. David J. Galles, Study notes of Data Structures and Algorithms

University of San Francisco (USF)Data Structures and Algorithms

Prof. David J. Galles

An in-depth explanation of connected components in graph theory. It covers the concepts of strongly connected graphs, connected components, and algorithms for finding connected components using depth-first search (dfs). The document also includes dfs algorithm implementation and examples.

Typology: Study notes

Pre 2010

Uploaded on 07/30/2009

koofers-user-7rn 🇺🇸

10 documents

1 / 25

This page cannot be seen from the preview

Don't miss anything!

CS245-2009S-21 Connected Components 1

21-0: Strongly Connected Graph

•Directed Path from every node to every other node

2 3

•Strongly Connected

21-1: Strongly Connected Graph

•Directed Path from every node to every other node

2 3

•Strongly Connected

21-2: Connected Components

•Subgraph (subset of the vertices) that is strongly connected.

6 8

21-3: Connected Components

Discover Study notes of Data Structures and Algorithms University of San Francisco (USF)

Partial preview of the text

Download Connected Components in Graph Theory - Prof. David J. Galles and more Study notes Data Structures and Algorithms in PDF only on Docsity!

21-0: Strongly Connected Graph

Directed Path from every node to every other node

Strongly Connected

21-1: Strongly Connected Graph

Directed Path from every node to every other node

Strongly Connected

21-2: Connected Components

Subgraph (subset of the vertices) that is strongly connected.

1 7

21-3: Connected Components

Subgraph (subset of the vertices) that is strongly connected.

1 7

6 8

21-4: Connected Components

Subgraph (subset of the vertices) that is strongly connected.

1 7

21-5: Connected Components

Subgraph (subset of the vertices) that is strongly connected.

1 7

6 8

21-6: Connected Components

Connected components of the graph are the largest possible strongly connected subgraphs
If we put each vertex in its own component – each component would be (trivially) strongly connected
- Those would not be the connected components of the graph – unless there were no larger connected subgraphs

21-12: DFS Example

d f

21-13: DFS Example

d 1 f

d f

d 1 f

d f

d 2 f

d f

21-15: DFS Example

d 1 f

d 3 f

d f

d 2 f

d f

d 1 f

d 3 f

d f

d 2 f

d 4 f

d 5 f 6

d f

21-19: DFS Example

d 1 f

d 3 f

d f

d 2 f

d 4 f 7

d 5 f 6

d f

d 1 f

d 3 f 8

d f

d 2 f

d 4 f 7

d 5 f 6

d f

21-21: DFS Example

d 1 f

d 3 f 8

d f

d 2 f 9

d 4 f 7

d 5 f 6

d f

1 7

6 8

d 1 f 10

d 3 f 8

d 11 f

d 12 f

d 2 f 9

d 4 f 7

d 5 f 6

d f

21-25: DFS Example

1 7

6 8

d 1 f 10

d 3 f 8

d 11 f

d 12 f 13

d 2 f 9

d 4 f 7

d 5 f 6

d f

1 7

6 8

d 1 f 10

d 3 f 8

d 11 f

d 12 f 13

d 2 f 9

d 4 f 7

d 5 f 6

d 14 f

21-27: DFS Example

1 7

6 8

d 1 f 10

d 3 f 8

d 11 f

d 12 f 13

d 2 f 9

d 4 f 7

d 5 f 6

d 14 f 15

d 1 f

d f

d f 21-31: DFS Example

d 1 f

d f

d 2 f

d f

d 1 f

d f

d 2 f

d 3 f

d f

d f 21-33: DFS Example

d 1 f

d 4 f

d f

d 2 f

d 3 f

d f

d 1 f

d 4 f 7

d f

d 2 f

d 3 f

d 5 f 6

d f 21-37: DFS Example

d 1 f

d 4 f 7

d f

d 2 f

d 3 f 8

d 5 f 6

d f

d 1 f

d 4 f 7

d f

d 2 f 9

d 3 f 8

d 5 f 6

d f 21-39: DFS Example

d 1 f 10

d 4 f 7

d f

d 2 f 9

d 3 f 8

d 5 f 6

d f

1 7

6 8

d 1 f 10

d 4 f 7

d 11 f

d 13 f

d 2 f 9

d 3 f 8

d 5 f 6

d 12 f 21-43: DFS Example

1 7

6 8

d 1 f 10

d 4 f 7

d 11 f

d 13 f 14

d 2 f 9

d 3 f 8

d 5 f 6

d 12 f

1 7

6 8

d 1 f 10

d 4 f 7

d 11 f

d 13 f 14

d 2 f 9

d 3 f 8

d 5 f 6

d 12 f 15 21-45: DFS Example

1 7

6 8

d 1 f 10

d 4 f 7

d 11 f 16

d 13 f 14

d 2 f 9

d 3 f 8

d 5 f 6

d 12 f 15 21-46: Using d[] & f[]

Given two vertices v 1 and v 2 , what do we know if f [v 2 ] < f [v 1 ]?

21-47: Using d[] & f[]

Given two vertices v 1 and v 2 , what do we know if f [v 2 ] < f [v 1 ]?
- Either:
  - Path from v 1 to v 2
    - Start from v 1
    - Eventually visit v 2
    - Finish v 2
    - Finish v 1

21-48: Using d[] & f[]

Connected Components in Graph Theory - Prof. David J. Galles, Study notes of Data Structures and Algorithms

Related documents

Partial preview of the text

Download Connected Components in Graph Theory - Prof. David J. Galles and more Study notes Data Structures and Algorithms in PDF only on Docsity!