Download or read book A Simple Polynomial Time Algorithm for a Convex Hull Problem Equivalent to Linear Programming written by Rutgers University. Laboratory for Computer Science Research and published by . This book was released on 1993 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Over the rationals, the general linear programming problem is equivalent to the convex hull problem of determining if a given m x n matrix H has a nontrivial nonnegative zero. We give a polynomial time algorithm that either finds a nontrivial nonnegative zero of H, or it obtains a hyperplane separating the column vectors of H from the origin. In particular, the algorithm provides an alternate proof of a strengthened version of Gordan's duality theorem, previously proved by the author. The algorithm which is motivated by this duality theorem is analogous to Karmarkar's algorithm but its analysis is much simpler."
Download or read book Interior point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Download or read book A General Convex Hull Algorithm with Linear Expected Time written by Judah Ben Rosen and published by . This book was released on 1989 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We transform the convex hull problem with n points in a d-dimensional Euclidean space into n independent linear programming problems of size (d+1) by n. These may be solved in polynomial time. Actually the expected time is O(n2). Combining this algorithm with the algorithm of Bentley et al which finds all the maximal vectors in linear expected time, we arrived at an algorithm which finds all the extreme points of the convex hull of a given set of n points in d-dimensional space in linear expected time.
Download or read book An O n Log2h Time Algorithm for the Three dimensional Convex Hull Problem written by Herbert Edelsbrunner and published by . This book was released on 1989 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics Advances written by Charles J. Colbourn and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: On March 28~31, 1994 (Farvardin 8~11, 1373 by Iranian calendar), the Twenty fifth Annual Iranian Mathematics Conference (AIMC25) was held at Sharif University of Technology in Tehran, Islamic Republic of Iran. Its sponsors in~ eluded the Iranian Mathematical Society, and the Department of Mathematical Sciences at Sharif University of Technology. Among the keynote speakers were Professor Dr. Andreas Dress and Professor Richard K. Guy. Their plenary lec~ tures on combinatorial themes were complemented by invited and contributed lectures in a Combinatorics Session. This book is a collection of refereed papers, submitted primarily by the participants after the conference. The topics covered are diverse, spanning a wide range of combinatorics and al~ lied areas in discrete mathematics. Perhaps the strength and variety of the pa~ pers here serve as the best indications that combinatorics is advancing quickly, and that the Iranian mathematics community contains very active contributors. We hope that you find the papers mathematically stimulating, and look forward to a long and productive growth of combinatorial mathematics in Iran.
Download or read book Computing and Combinatorics written by Lusheng Wang and published by Springer Science & Business Media. This book was released on 2005-08-04 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed proceedings of the 11th Annual International Computing and Combinatorics Conference, COCOON 2005, held in Kunming, China in August 2005. The 96 revised full papers presented together with abstracts of 3 invited talks were carefully reviewed and selected from 353 submissions. The papers cover most aspects of theoretical computer science and combinatorics related to computing and are organized in topical sections on bioinformatics, networks, string algorithms, scheduling, complexity, steiner trees, graph drawing and layout design, quantum computing, randomized algorithms, geometry, codes, finance, facility location, graph theory, graph algorithms.
Download or read book A polynomial time algorithm for solving systems of linear inequalities with two variables per inequality written by Stanford University. Computer Science Department and published by . This book was released on 1979 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a constructive algorithm for solving systems of linear inequalities (LI) with at most two variables per inequality. The algorithm is polynomial in the size of the input. The LI problem is of importance in complexity theory since it is polynomial time equivalent to linear programming. The subclass of LI treated in this paper is also of practical interest in mechanical verification systems, and we believe that the ideas presented can be extended to the general LI problem. (Author).
Download or read book An Algorithmic Theory of Numbers Graphs and Convexity written by Laszlo Lovasz and published by SIAM. This book was released on 1987-01-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.
Download or read book Algebra Geometry and Software Systems written by Michael Joswig and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
Download or read book A Simple Polynomial time Algorithm is an Alternative to Linear SVM written by Amit Kagan and published by . This book was released on 2006 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Understanding and Using Linear Programming written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2007-07-04 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".
Download or read book Logic Based Program Synthesis and Transformation written by M. Leuschel and published by Springer Science & Business Media. This book was released on 2003-06-18 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 12th International Workshop on Logic Based Program Synthesis and Transformation, LOPSTR 2002, held in Madrid, Spain in September 2002. The 15 revised full papers presented together with 7 abstracts were carefully selected during two rounds of reviewing and revision from 40 submissions. The papers are organized in topical sections on debugging and types, tabling and constraints, abstract interpretation, program refinement, verification, partial evaluation, and rewriting and object-oriented development.
Download or read book Algorithms For Dummies written by John Paul Mueller and published by John Wiley & Sons. This book was released on 2017-04-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how algorithms shape and impact our digital world All data, big or small, starts with algorithms. Algorithms are mathematical equations that determine what we see—based on our likes, dislikes, queries, views, interests, relationships, and more—online. They are, in a sense, the electronic gatekeepers to our digital, as well as our physical, world. This book demystifies the subject of algorithms so you can understand how important they are business and scientific decision making. Algorithms for Dummies is a clear and concise primer for everyday people who are interested in algorithms and how they impact our digital lives. Based on the fact that we already live in a world where algorithms are behind most of the technology we use, this book offers eye-opening information on the pervasiveness and importance of this mathematical science—how it plays out in our everyday digestion of news and entertainment, as well as in its influence on our social interactions and consumerism. Readers even learn how to program an algorithm using Python! Become well-versed in the major areas comprising algorithms Examine the incredible history behind algorithms Get familiar with real-world applications of problem-solving procedures Experience hands-on development of an algorithm from start to finish with Python If you have a nagging curiosity about why an ad for that hammock you checked out on Amazon is appearing on your Facebook page, you'll find Algorithm for Dummies to be an enlightening introduction to this integral realm of math, science, and business.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Python Algorithms written by Magnus Lie Hetland and published by Apress. This book was released on 2011-02-27 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Python Algorithms explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science, but in a highly pedagogic and readable manner. The book covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data structures that are built into the Python language are explained, and the user is shown how to implement and evaluate others himself.
Download or read book Geometric Algorithms and Combinatorial Optimization written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. 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.
Download or read book Computational Geometry written by Mark de Berg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study.
