Golden Ticket: Chapter 3

For Your Enjoyment

Describe an algorithm for computing the closest distance between two people in Frenemy. What is the time complexity of this algorithm?
Describe an algorithm for verifying that k vertices are a clique. What is the time complexity of this algorithm?
Describe an algorithm for finding the largest clique in a graph. What is the time complexity of this algorithm?
Describe an algorithm for determining if an Eulerian Circuit exists. What is the time complexity of this algorithm?
Which of the problems above are decision problems?
How can we turn a non-decision problem into a decision problem?
Suppose we had an oracle that would tell us the correct answer to any decision problem. When the answer is yes, the oracle will show us a solution that we must verify. Given such an oracle, which of the above problems can we now solve more efficiently?
P: Problems that can be solved in polynomial time without an oracle.
NP: Problems that can be solved in polynomial time with an oracle.
Which of the above problems are in P?
Which of the above problems are in NP?
Does P = NP? No one knows for sure! This is the most important open question in computer science.
What would it take to show that P = NP?
What would it take to show that P ≠ NP?