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For Wednesday

For Wednesday. Read 10.1 No homework. Program 4. Any questions?. Exam 1. In-class portion on Friday Take-home due Monday Questions?. Paper 2. Any questions? Topic paragraph due Wednesday, Nov 8. Graph Searching. Depth-first Breadth-first Best-first. Applications of Searching.

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For Wednesday

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  1. For Wednesday • Read 10.1 • No homework

  2. Program 4 • Any questions?

  3. Exam 1 • In-class portion on Friday • Take-home due Monday • Questions?

  4. Paper 2 • Any questions? • Topic paragraph due Wednesday, Nov 8

  5. Graph Searching • Depth-first • Breadth-first • Best-first

  6. Applications of Searching • Connectivity in an undirected graph

  7. Bi-Connectivity • What’s the problem? • How can it be solved using DFS?

  8. Euler Circuits • What’s the problem? • How can it be solved using DFS?

  9. Difficulty Levels • Undecidable • Example is halting problem • Intractable • Example is ? • Exponential problems are considered intractable. Why?

  10. Another Class of Intractable Problems • Polynomial problems are considered tractable. • What does NP mean?

  11. Non-deterministic Polynomial • A deterministic machine must always make a single choice. • Suppose you had a non-deterministic computer. • Then you could “pick” all of the different choices at once (or automatically pick the best solution).

  12. The Class NP • Can determine that a solution is the correct solution in polynomial time. • All problems with polynomial time solutions fit into this class. • Some decidable problems do not. Consider problems for which the solution is of exponential length.

  13. The Big Question • Are there problem in NP that are not in P? • Brings us to the class of NP-complete and NP-hard problems. • NP-complete problems are reducible to one another.

  14. Examples • Traveling Salesman • Hamiltonian Cycle • Satisfiability (technically, 3Sat) • Graph coloring • Knapsack • Bin packing

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