08 - np-complete sequencing problems- hamiltonian cycle, traveling salesman problem

08 - NP-complete sequencing problems- Hamiltonian cycle, traveling salesman problem
Download Document
Showing pages : 1 - 2 of 4
This preview has blurred sections. Sign up to view the full version! View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3/24/08 - NP-complete sequencing pro... NP: problems whose solution can be e f ciently (poly-time) verifed. Ex: Compositeness: Given n-bit number x, in x composite? Hint: a pair y,z > 1 such that yz = x. NP-Complete: a problem X which is in NP and every other problem Y in NP has a poly-time reduction FROM Y TO X. Ex. Ind. Set, 3 SAT. Alt de¡: a problem X which is in NP and there exists NPC problem Y which has a poly-time reduction ¡rom Y to X. 2 easy reductions ¡rom ind. set. (1) CLIQUE: Given undirected graph G = (V, E) and a number k > 0. Output yes i¡ G has a subgraph H with k vertices and every 2 vertices o¡ H are joined by an edge. (H is a k-clique.) Take (G, k) an instance o¡ IND. SET. Construct G ̅ which has same vertex set and (u,v) E(G ̅ ) <=> (u,v) E(G). (1) Reduction runs in poly-time. YES! O(n 2 ) (2) I¡ G has k-ind set, G ̅ has a k-clique....
View Full Document