# 12. P NP - graph: (NN-1) P and NP P NP-Complete NP P and NP...

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P and NP P Stands for solvable in polynomial time, e.g., Heapsort for N elements: θ(NlogN) = O(N 2 ) All pairs shortest distance (Floyd-Warshall) for an N node graph: θ(N 3 ) Matrix Multiplication (N x N): θ(N 3 )

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P and NP NP Stands stand for Nondeterministic polynomial time Problems for which a solution can be tested in polynomial time All problems in P are in NP Some problems are not in NP, e.g., Display permutations of an N element set: θ(N!) Display all minimum spanning trees of a

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Unformatted text preview: graph: (NN-1) P and NP P NP-Complete NP P and NP NP Complete Stands for the hardest decision problems in NP If any NP-Complete problem can be solved in polynomial time, then P = NP Some examples of NP-Complete are: Is there a traveling salesperson tour for graph G of cost less than K? Is there a Steiner Tree for graph G of cost less than K? P and NP NP-Complete NP CO-NP P C0-NP-Complete...
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## This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Fall '08 term at Southern Illinois University Edwardsville.

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12. P NP - graph: (NN-1) P and NP P NP-Complete NP P and NP...

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