# Lecture29 - Today NP-completeness CSE 421 Algorithms...

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1 CSE 421 Algorithms Richard Anderson Lecture 29 NP-Completeness and course wrap-up Today • NP-completeness – Reductions – Problem Thresholds – Number problems – What is NP? – What we don’t know about NP-completeness • Course summary • Evaluations NP-Completeness Reductions • If X is NP-Complete, Y is in NP, and X < P Y, then Y is NP-Complete Hamiltonian Circuit, Hamiltonian Path How do you show that Hamiltonian Path is NP-Complete? 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 HamPath < P DirHamPath How do you show that Directed Hamiltonian Path is NP-Complete?

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2 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
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Lecture29 - Today NP-completeness CSE 421 Algorithms...

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