t10 - CS3230 Tutorial 10 1. Consider the following problem:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS3230 Tutorial 10 1. Consider the following problem: Input: Given a weighted graph G , two vertices u and v in G , and a value d . Question: Is there a path from u to v of weight at most d ? Is the above problem in NP? Could it be NP-complete? 2. In class we saw that it is open at present whether P = NP or not. It is also open whether NP = EXP or not. Is it possible that both P = NP and NP = EXP are true? 3. It can be shown that knapsack problem is NP-complete. Thus, if knapsack problem can be solved in polynomial time, then all problems in NP can be solved in polynomial time. Professor S claimed that he could solve the discrete knapsack problem in time proportional to C * n (see the dynamic programming algorithm done in class), where C is the capacity of the knapsack and n is the number of objects in the problem. Thus the discrete knapsack problem is in P. Thus, Professor S claimed that he has shown P=NP. Could you find a flaw in his argu- ment? 4. Show that testing whether a graph
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

t10 - CS3230 Tutorial 10 1. Consider the following problem:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online