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CSE 421
Algorithms
Richard Anderson
Lecture 29
NPCompleteness and course wrapup
Today
• NPcompleteness
– Reductions
– Problem Thresholds
– Number problems
– What is NP?
– What we don’t know about NPcompleteness
• Course summary
• Evaluations
NPCompleteness Reductions
• If X is NPComplete, Y is in NP, and
X <
P
Y, then Y is NPComplete
Hamiltonian Circuit,
Hamiltonian Path
How do you show that Hamiltonian Path is NPComplete?
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 NPComplete?
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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
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 Fall '06
 RichardAnderson
 Algorithms

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