This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: P ic tu r e 8 Click to edit Master subtitle style PCPs and Inapproximability Introduction P ic tu r e 8 My T. Thai [email protected] My T. Thai [email protected] 22 Why Approximation Algorithms Ø Problems that we cannot find an optimal solution in a polynomial time q Eg: Set Cover, Bin Packing Ø Need to find a nearoptimal solution: q Heuristic q Approximation algorithms: § This gives us a guarantee approximation ratio P ic tu r e 8 My T. Thai [email protected] My T. Thai [email protected] 33 Combinatorial Optimization Ø The study of finding the “best” object from within some finite space of objects, eg: q Shortest path : Given a graph with edge costs and a pair of nodes, find the shortest path (least costs) between them q Traveling salesman : Given a complete graph with nonnegative edge costs, find a minimum cost cycle visiting every vertex exactly once q Maximum Network Lifetime : Given a wireless sensor networks and a set of targets, find a schedule of these sensors to maximize network lifetime P ic tu r e 8 My T. Thai [email protected] My T. Thai [email protected] 44 In P or not in P? Informal Definitions: Ø The class P consists of those problems that are solvable in polynomial time, i.e. O(nk) for some constant k where n is the size of the input. Ø The class NP consists of those problems that are “verifiable” in polynomial time: q Given a certificate of a solution, then we can verify that the certificate is correct in polynomial time P ic tu r e 8 My T. Thai [email protected] My T. Thai [email protected] 55 In P or not in P: Examples Ø In P: q Shortest path q Minimum Spanning Tree Ø Not in P (NP): q Vertex Cover q Traveling salesman q Minimum Connected Dominating Set P ic tu r e 8 My T. Thai [email protected] My T. Thai [email protected] 66 Approximation Algorithms Ø An algorithm that returns...
View
Full
Document
This note was uploaded on 05/20/2011 for the course CIS 6930 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Algorithms

Click to edit the document details