08 - NP-complete sequencing problems- Hamiltonian cycle, traveling salesman problem

# 08 - NP-complete sequencing problems- Hamiltonian cycle, traveling salesman problem

This preview shows pages 1–2. Sign up to view the full content.

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. (3) I± G has no k-ind set, G

This preview has intentionally 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.

## This note was uploaded on 10/02/2008 for the course CS 482 taught by Professor Kleinberg during the Spring '08 term at Cornell.

### Page1 / 4

08 - NP-complete sequencing problems- Hamiltonian cycle, traveling salesman problem

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online