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Lecture 11

Lecture 11. CSE 331 Sep 24, 2012. Puzzle. Prove that any algorithm for the SMP takes Ω(n 2 ) time. Wednesday. No lecture or OH till 6pm. Online OH at 9:30pm. Main Steps in Algorithm Design. Problem Statement. Problem Definition. Algorithm. n!. “ Implementation ”. Analysis.

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Lecture 11

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  1. Lecture 11 CSE 331 Sep 24, 2012

  2. Puzzle Prove that any algorithm for the SMP takes Ω(n2) time

  3. Wednesday No lecture or OH till 6pm Online OH at 9:30pm

  4. Main Steps in Algorithm Design Problem Statement Problem Definition Algorithm n! “Implementation” Analysis Correctness Analysis

  5. Reading Assignments Sec 1.1 and Chap. 2 in [KT]

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

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

  8. Graphs are omnipresent Airline Route maps

  9. What does this graph represent? Internet

  10. And this one? Math articles on Wikipedia

  11. And this one?

  12. Rest of today’s agenda Basic Graph definitions

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

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

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

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

  17. Formally define everything http://imgs.xkcd.com/comics/geeks_and_nerds.png

  18. Tree Connected undirected graph with no cycles

  19. Rooted Tree

  20. 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”

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

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