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CSE 421
Algorithms
Richard Anderson
Lecture 28
NPCompleteness
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View Full Document Populating the NPCompleteness
Universe
•
Circuit Sat <
P
3SAT
•
3SAT <
P
Independent Set
•
3SAT <
P
Vertex Cover
•
Independent Set <
P
Clique
•
3SAT <
P
Hamiltonian Circuit
•
Hamiltonian Circuit <
P
Traveling Salesman
•
3SAT <
P
Integer Linear Programming
•
3SAT <
P
Graph Coloring
•
3SAT <
P
Subset Sum
•
Subset Sum <
P
Scheduling with Release times and
deadlines
Cook’s Theorem
•
The Circuit Satisfiability Problem is NP
Complete
•
Circuit Satisfiability
–
Given a boolean circuit, determine if there is
an assignment of boolean values to the input
to make the output true
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View Full Document Circuit SAT
AND
OR
AND
AND
OR
OR
AND
NOT
OR
NOT
x
1
x
2
x
3
x
4
x
5
AND
AND
NOT
NOT
AND
OR
NOT
AND
OR
AND
Satisfying assignment
x
1
= T, x
2
= F, x
3
= F
x
4
= T, x
5
= T
Find a satisfying assignment
Proof of Cook’s Theorem
•
Reduce an arbitrary problem Y in NP to X
•
Let A be a nondeterministic polynomial
time algorithm for Y
•
Convert A to a circuit, so that Y is a Yes
instance iff and only if the circuit is
satisfiable
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This note was uploaded on 02/25/2012 for the course CSE 421 taught by Professor Richardanderson during the Fall '06 term at University of Washington.
 Fall '06
 RichardAnderson
 Algorithms

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