This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Computer Science E207 A Reduction 1. NPcompleteness. A language L is said to be NPcomplete iff L is in NP ; and L is NPhard (i.e. every language in NP is reducible to L in polynomial time). To show L is in NP : Show that L has succinct certificates that can be nondeterministically guessed; and Give a polynomial time algorithm that checks the certificates. To show L is NPhard: Choose a known NPcomplete language L to reduce from. Reduce L to L . Show that the reduction can be done in polynomial time. What are some known NPcomplete languages? Sat, 3Sat, Integer Linear Programming, Vertex Cover, Clique, Independent Set . What should the reduction look like? We begin with a problem X and a known NPcomplete problem X . We want to show that if we had some deterministic polynomial time algorithm for solving X , we could use it to solve X in deterministic polynomial time. To do this, we have to be able to transform every instance of the problem X into an instance of the problem...
View
Full Document
 Fall '09
 Computer Science, Graph Theory, Vertex, Computational complexity theory, independent set, half cover

Click to edit the document details