Lecture 6 - NP-Completeness

Question 1

If one NP-Complete problem s solvable in poly-time then what can we say about the rest of them.

Answer 1

That they’re all solvable in polytime

Question 2

If one of NP-Complete problems is proven to be intractable, then what can we say about the rest of them?

Answer 2

That all of them are intracable

Question 3

What is the current belief about NP-Complete problems?

Answer 3

That they’re all intractable, although no one has managed to prove this

Question 4

What do we think about NP-Complete problems

Answer 4

That they’re all equally hard to solve.

Question 5

What are the causes of intractability?

Answer 5

• polynomial time is not sufficient in order to discover a solution
• solution itself is so large that exponential time is needed to output it
• we will be concerned with the first one

Question 6

What is undecidable?

Answer 6

Can’t be solved.

Question 7

What is intractable?

Answer 7

Solveable but not in poly time.

Question 8

Example of an intractable problem?

Answer 8

Roadblock

Question 9

So what are NP problems?

Answer 9

They’re either poly time solvable or intractable.

Question 10

What problems does np-completeness primarily deal with?

Answer 10

decision problems, often however corresponding to search or optimisation problems via setting target values

Question 11

optimisation problem or search problem be solved in poly time?

Answer 11

means the equivalent decision problem can be solved in poly-time too.