'Vertex cover' presentation slideshows

The Ferry Cover Problem

1.53k views • 134 slides

Reducibility and NP-Completeness

Reducibility and NP-Completeness. Computational Complexity Theory. Computational Complexity Theory is the study of how much of a given resource (such as time, space, parallelism, algebraic operations, communication) is required to solve important problems. Classification of Problems.

1.23k views • 100 slides

On the Compressibility of NP instances and Cryptographic Applications,

On the Compressibility of NP instances and Cryptographic Applications,. Danny Harnik. Moni Naor. Weizmann Institute of Science. Technion. Key Idea of Cryptography. Use the intractability of some problems for the advantage of constructing secure systems.

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CSE 421 Algorithms

CSE 421 Algorithms. Richard Anderson Lecture 27 NP Completeness. Algorithms vs. Lower bounds. Algorithmic Theory What we can compute I can solve problem X with resources R Proofs are almost always to give an algorithm that meets the resource bounds Lower bounds

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Approximation Algorithm

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Approximation Algorithms

Approximation Algorithms. Chapter 1- Introduction. Why Approximation Algorithms. Problems that we cannot find an optimal solution in a polynomial time Eg: Set Cover, Bin Packing Need to find a near-optimal solution: Heuristic Approximation algorithms:

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Approximation Algorithms

Approximation Algorithms. Chapter 11. Approximation Algorithms. Q. Suppose I need to solve an NP-hard problem. What should I do? A. Theory says you're unlikely to find a poly-time algorithm. Must sacrifice one of three desired features. Solve problem to optimality.

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Design and Analysis of Algorithms Approximation algorithms for NP-complete problems

Design and Analysis of Algorithms Approximation algorithms for NP-complete problems. Haidong Xue Summer 2012, at GSU. Approximation algorithms for NPC problems. If a problem is NP-complete, there is very likely no polynomial-time algorithm to find an optimal solution

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Graph Theoretic Concepts and Algorithms for Bioinformatics

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More NP-complete Problems

More NP-complete Problems. Theorem:. (proven in previous class). If: Language is NP-complete Language is in NP is polynomial time reducible to. Then: is NP-complete. Using the previous theorem, we will prove that 2 problems are NP-complete:. Vertex-Cover.

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NP-complete and NP-hard problems

NP-complete and NP-hard problems. Transitivity of polynomial-time many-one reductions Concept of Completeness and hardness for a complexity class Definition of complexity class NP NP-complete and NP-hard problems. P 1 ? p P 2 & P 2 ? p P 3 ? P 1 ? p P 3.

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Trusted Computing Amidst Untrustworthy Intermediaries

Trusted Computing Amidst Untrustworthy Intermediaries. Mike Langston Department of Computer Science University of Tennessee currently on leave to Computer Science and Mathematics Division Oak Ridge National Laboratory USA. Overview. Highly Parallel Scalable Network Variable Topology

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PCPs and Inapproximability

PCPs and Inapproximability. Introduction. Why Approximation Algorithms. Problems that we cannot find an optimal solution in a polynomial time Eg: Set Cover, Bin Packing Need to find a near-optimal solution: Heuristic Approximation algorithms: This gives us a guarantee approximation ratio.

364 views • 24 slides

Preprocessing Graph Problems When Does a Small Vertex Cover Help?

Preprocessing Graph Problems When Does a Small Vertex Cover Help?. Bart M. P. Jansen Joint work with Fedor V. Fomin & Micha? Pilipczuk. June 2012, Dagstuhl Seminar 12241. Motivation. Graph structure affects problem complexity

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NP-complete examples

Fall 2009. NP-complete examples. Xiao Linfu. CSC3130 Tutorial 11. lfxiao@cse.cuhk.edu.hk. Department of Computer Science & Engineering. Outline. Review of P, NP, NP-C 2 problem s Double-SAT Dominating set http://en.wikipedia.org/wiki/Dominating_set_problem. Relations. hard. NP-C.

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Advanced Approximation Algorithms I

Advanced Approximation Algorithms I. Weighted Vertex Cover Set Cover Coloring 3-colorable Graphs. Weighted Vertex Cover. Given an undirected graph G=(V,E) and vertex weights w:V->R , find subset S of V such that and is as small as possible. Weighted Vertex Cover. 2. 2. 4.

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Example Question on Linear Program, Dual and NP-Complete Proof

Example Question on Linear Program, Dual and NP-Complete Proof . COT5405 Spring 11. Question. Given an undirected connected graph G = ( V,E ) and a positive integer k ? | V|. T wo vertices u and v are connected if and only if there exists at least one path from u to v.

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An NP-completeness Example

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NP-Completeness

NP-Completeness. Section 7.1 Fri, Dec 9, 2005. Polynomial-Time Reductions. A function f : ? * ? ? * is polynomial-time computable if there exists a polynomially bounded Turing Machine that computes f .

206 views • 7 slides