1. Lecture 10
CSE 331
Sep 20, 2017

2. Mini Project choice due Sep 25

3. A generic tool to abstract out problems
Up Next….
Problem Statement
A generic tool to abstract out problems
Problem Definition
Algorithm
“Implementation”
Analysis

4. Relationship: Mention in other’s program
Graphs
Representation of relationships between pairs of entities/elements
Edge
Entities: News hosts
Relationship: Mention in other’s program
Vertex/Node

5. Graphs are omnipresent
Airline Route maps

6. What does this graph represent?
Internet

7. And this one?
Math articles on Wikipedia

8. And this one?

9. Rest of today’s agenda
Basic Graph definitions

10. Paths , , Sequence of vertices connected by edges Connected
Path length 3 ,

11. Connectivity
u and w are connected iff there is a path between them
A graph is connected iff all pairs of vertices are connected

12. Connected Graphs
Every pair of vertices has a path between them

13. Cycles
Sequence of k vertices connected by edges, first k-1 are distinct ,

15. Formally define everything

16. Rest of Today’s agenda Prove n vertex tree has n-1 edges
Formal definitions of graphs, paths, cycles, connectivity
and trees
Prove n vertex tree has n-1 edges
Algorithms for checking connectivity

17. Tree
Connected undirected graph with no cycles

18. Rooted Tree

19. A rooted tree AC’s child=SG Pick any vertex as root SG’s parent=AC
Let the rest of the tree hang under “gravity”

20. Rest of Today’s agenda Prove n vertex tree has n-1 edges
Algorithms for checking connectivity

21. Checking by inspection

22. What about large graphs?
Are s and t connected?

23. Brute-force algorithm?
List all possible vertex sequences between s and t
nn such sequences
Check if any is a path between s and t

24. Algorithm motivation
all