Introduction - P ic tu r e 8 Click to edit Master subtitle...

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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 near-optimal 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...
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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.

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Introduction - P ic tu r e 8 Click to edit Master subtitle...

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