Lecture28 - CSE 421 Algorithms Richard Anderson Lecture 28...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE 421 Algorithms Richard Anderson Lecture 28 NP-Completeness
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Populating the NP-Completeness Universe Circuit Sat < P 3-SAT 3-SAT < P Independent Set 3-SAT < P Vertex Cover Independent Set < P Clique 3-SAT < P Hamiltonian Circuit Hamiltonian Circuit < P Traveling Salesman 3-SAT < P Integer Linear Programming 3-SAT < P Graph Coloring 3-SAT < P Subset Sum Subset Sum < P Scheduling with Release times and deadlines
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
Proof of Cook’s Theorem Reduce an arbitrary problem Y in NP to X Let A be a non-deterministic 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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 22

Lecture28 - CSE 421 Algorithms Richard Anderson Lecture 28...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online