Computer Networking: A Top-Down Approach (7th Edition)
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ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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The knapsack problem (KP) can be solved with dynamic programming (DP) in O(nS), where n is the number of items and S the knapsack capacity.
O Such a complexity is not polynomial with respect to the size the instance when a binary encoding is used. Thus, the algorithm is not (strictly) polynomial
O f the instance is encoded in unary, such a complexity is polynomial. Thus, one can claim that the DP algorithm is polynomial in the general case.
O Since the problem is NP-hard, it cannot be solved in polynomial time even if the instance is encoded in unary. unless P-NP.
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