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Unformatted text preview: 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 NPcomplete? Ans: Yes, it is in P (and thus in NP), as we can solve the problem using Dijkstra’s algorithm in polynomial time. Yes, it could be NPcomplete, if P=NP. If P 6 = NP, then it will not be NPcomplete. 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? Ans: No. As that would imply P = EXP , which is known not to be true. 3. It can be shown that discrete knapsack problem is NPcomplete. Thus, if discrete knap sack 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....
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 Fall '10
 sanjay
 Algorithms, Computational complexity theory, polynomial time, Professor S, discrete knapsack problem

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