Lecture29 - CSE 421 Algorithms Richard Anderson Lecture 29...

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CSE 421 Algorithms Richard Anderson Lecture 29 NP-Completeness and course wrap-up
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Today NP-completeness Reductions Problem Thresholds Number problems What is NP? What we don’t know about NP-completeness Course summary Evaluations
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NP-Completeness Reductions If X is NP-Complete, Y is in NP, and X < P Y, then Y is NP-Complete
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Hamiltonian Circuit, Hamiltonian Path How do you show that Hamiltonian Path is NP-Complete?
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Local Modification Convert G to G’ Pick a vertex v Replace v by v’ and v’’ If (u,v) is an edge, include edges (u, v’), (u, v’’) G’ has a Hamiltonian Path from v’ to v’’ iff G has a Hamiltonian Circuit
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HamPath < P DirHamPath How do you show that Directed Hamiltonian Path is NP-Complete?
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Problem definition Given a graph G, does G have an independent set? Given a graph G, does G have an independent set of size 7? Given a graph G, and an integer K, does G have an independent set of size K?
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Graph Coloring NP-Complete Graph K-coloring Graph 3-coloring Polynomial Graph 2-Coloring
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