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Geometric Approximation Algorithms

2011 Computers
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Release : 2011
Genre : Computers
Kind : eBook
Book Rating : 115/5 ( reviews)

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Book Synopsis Geometric Approximation Algorithms by : Sariel Har-Peled

Download or read book Geometric Approximation Algorithms written by Sariel Har-Peled. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

Geometric Approximation Algorithms

2011 Mathematics
Download Geometric Approximation Algorithms PDF Online Free

Author :
Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 562/5 ( reviews)

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Book Synopsis Geometric Approximation Algorithms by : Sariel Har-Peled

Download or read book Geometric Approximation Algorithms written by Sariel Har-Peled. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: Exact algorithms for dealing with geometric objects are slow, complicated and hard to implement in practice. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms are simple, fast, and more robust than their exact counterparts. This book looks at geometric approximation algorithms.

Geometric Approximation Algorithms

2011 Mathematics
Download Geometric Approximation Algorithms PDF Online Free

Author :
Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 009/5 ( reviews)

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Book Synopsis Geometric Approximation Algorithms by : Sariel Har-Peled

Download or read book Geometric Approximation Algorithms written by Sariel Har-Peled. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are surveyed.

Geometric Algorithms and Combinatorial Optimization

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 819/5 ( reviews)

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Book Synopsis Geometric Algorithms and Combinatorial Optimization by : Martin Grötschel

Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.

Geometric Approximation Algorithms in the Online and Data Stream Models

2008
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Release : 2008
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Geometric Approximation Algorithms in the Online and Data Stream Models by : Hamid Zarrabi-Zadeh

Download or read book Geometric Approximation Algorithms in the Online and Data Stream Models written by Hamid Zarrabi-Zadeh. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: The online and data stream models of computation have recently attracted considerable research attention due to many real-world applications in various areas such as data mining, machine learning, distributed computing, and robotics. In both these models, input items arrive one at a time, and the algorithms must decide based on the partial data received so far, without any secure information about the data that will arrive in the future. In this thesis, we investigate efficient algorithms for a number of fundamental geometric optimization problems in the online and data stream models. The problems studied in this thesis can be divided into two major categories: geometric clustering and computing various extent measures of a set of points.

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