For Wednesday No reading Research paper topic due on Blackboard - - PowerPoint PPT Presentation

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For Wednesday No reading Research paper topic due on Blackboard - - PowerPoint PPT Presentation

For Wednesday No reading Research paper topic due on Blackboard Homework: Weiss, chapter 9, exercises 15-16 Program 4 Any questions? Research Paper Questions? Exam 2 Graph Searching Depth-first Breadth-first


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SLIDE 1

For Wednesday

  • No reading
  • Research paper topic due on Blackboard
  • Homework:

– Weiss, chapter 9, exercises 15-16

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SLIDE 2

Program 4

  • Any questions?
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SLIDE 3

Research Paper

  • Questions?
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SLIDE 4

Exam 2

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SLIDE 5

Graph Searching

  • Depth-first
  • Breadth-first
  • Best-first
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SLIDE 6

Applications of Searching

  • Connectivity in an undirected graph
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SLIDE 7

Bi-Connectivity

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SLIDE 8

Euler Circuits

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SLIDE 9

Difficulty Levels

  • Undecidable

– Example is halting problem

  • Intractable

– Example is ?

  • Exponential problems are considered
  • intractable. Why?
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SLIDE 10

Another Class of Intractable Problems

  • Polynomial problems are considered

tractable.

  • What does NP mean?
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SLIDE 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).

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SLIDE 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.

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SLIDE 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.

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SLIDE 14

Examples

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