Geometric Algorithms And Combinatorial Optimization

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Geometric Algorithms And Combinatorial Optimization

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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Geometric Algorithms And Combinatorial Optimization written by Martin Grötschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.

Geometric Embeddings Geometric Algorithms And Combinatorial Optimization

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Author : James Russell Lee
language : en
Publisher:
Release Date : 2006

Geometric Embeddings Geometric Algorithms And Combinatorial Optimization written by James Russell Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

The present thesis is divided into two parts which address questions of both types (i.e. combinatorial data and geometric data, respectively), leading to new algorithms for a variety of well-known combinatorial problems, new connections between geometry and computer science, and new geometric and analytic information about some classical mathematical objects.

Geometric Methods And Optimization Problems

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Author : Vladimir Boltyanski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

Geometric Methods And Optimization Problems written by Vladimir Boltyanski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.

Journal Of The Acm

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Author :
language : en
Publisher:
Release Date : 2001

Journal Of The Acm written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.

Proceedings Of The Acm Symposium On Theory Of Computing

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Author :
language : en
Publisher:
Release Date : 2007

Proceedings Of The Acm Symposium On Theory Of Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Formal languages categories.

Siam Journal On Computing

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Author : Society for Industrial and Applied Mathematics
language : en
Publisher:
Release Date : 2006

Siam Journal On Computing written by Society for Industrial and Applied Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Electronic data processing categories.

Combinatorial Geometry

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Author : János Pach
language : en
Publisher: Wiley-Interscience
Release Date : 1995-10-20

Combinatorial Geometry written by János Pach and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-20 with Mathematics categories.

How many objects of a given shape and size can be packed into a large box of fixed volume? Can one plant n trees in an orchard, not all along the same line, so that every line determined by two trees will pass through a third? These questions, raised by Hilbert and Sylvester roughly one hundred years ago, have generated a lot of interest among professional and amateur mathematicians and scientists. They have led to the birth of a new mathematical discipline with close ties to classical geometry and number theory, and with many applications in coding theory, potential theory, computational geometry, computer graphics, robotics , etc. Combinatorial Geometry offers a self-contained introduction to this rapidly developing field, where combinatorial and probabilistic (counting) methods play a crucial role. This book has grown out of the material of both undergraduate and graduate courses in mathematics and computer science given by János Pach at the Courant Institute of Mathematical Sciences, New York University. Divided into two parts— Arrangements of Convex Sets and Arrangements of Points and Lines—it presents and explains some of the most important and ingenious results in combinatorial geometry, including: Dowker’s theorems Fáry’s theorem Fejes Tóth’ stheorems Methods of Blichtfeldt and Rogers Minkowski—Hlawka theorem Koebe’s representation theorem Lipton—Tarjan separator theorem Theorems of Erd???s, Turán, and Ramsey Szemerédi’s regularity lemma Szemerédi—Trotter theorems Methods of Clarkson, Edelsbrunner, Guibas, Sharir, and Welzl Counterexample to Borsuk’s conjecture

Algorithms In Combinatorial Geometry

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Author : Herbert Edelsbrunner
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-07-31

Algorithms In Combinatorial Geometry written by Herbert Edelsbrunner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-07-31 with Computers categories.

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Proceedings Of The 34th Annual Acm Symposium On The Theory Of Computing

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Author : John H. Reif
language : en
Publisher:
Release Date : 2002

Proceedings Of The 34th Annual Acm Symposium On The Theory Of Computing written by John H. Reif and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computable complexity categories.

Applied Mathematical Programming And Modeling Iii Apmod95

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Author :
language : en
Publisher:
Release Date : 1998

Applied Mathematical Programming And Modeling Iii Apmod95 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematical models categories.