For Wednesday

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

• Whats the problem?
• How can it be solved using DFS?

8
Euler Circuits

• Whats 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