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Lecture 11

Lecture 11. CSE 331 Sep 25, 2009. Homeworks. Please hand in your HW 2 now. HW 3 and graded HW 1 at the end of class. Graphs. Representation of relationships between pairs of entities/elements. # vertices = n #edges = m. Edge. Vertex. Paths. ,.

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Lecture 11

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  1. Lecture 11 CSE 331 Sep 25, 2009

  2. Homeworks Please hand in your HW 2 now HW 3 and graded HW 1 at the end of class

  3. Graphs Representation of relationships between pairs of entities/elements # vertices = n #edges = m Edge Vertex

  4. Paths , Sequence of (distinct) vertices connected by edges Connected Path length 3 , , ,

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

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

  7. Tree Connected undirected graph with no cycles

  8. Rooted Tree

  9. A rooted tree How many rooted trees can an n vertex tree have? AC’s child=SG Pick any vertex as root SG’s parent=AC Let the rest of the tree hang under “gravity”

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

  11. Checking by inspection

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

  13. Brute-force algorithm? List all possible vertex sequences between s and t 2n such sequences Check if any is a path between s and t

  14. Algorithm motivation all

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