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Author:
Publisher: Elsevier
ISBN: 0080867650
Category : Mathematics
Languages : en
Pages : 255
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Book Description
Algorithmic Aspects of Combinatorics
Author:
Publisher: Elsevier
ISBN: 0080867650
Category : Mathematics
Languages : en
Pages : 255
Get Book Here
Book Description
Algorithmic Aspects of Combinatorics
Author: Donald L. Kreher
Publisher: CRC Press
ISBN: 9780849339882
Category : Mathematics
Languages : en
Pages : 346
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Book Description
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as: Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
Author: Victor Bryant
Publisher: Cambridge University Press
ISBN: 9780521429979
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Combinatorics is a broad and important area of mathematics, and this textbook provides the beginner with the ideal introduction to many of the different aspects of the subject.
Author: Francine Blanchet-Sadri
Publisher: CRC Press
ISBN: 1420060937
Category : Computers
Languages : en
Pages : 392
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Book Description
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing. Delving
Author: Martin Grötschel
Publisher: Springer Science & Business Media
ISBN: 3642978819
Category : Mathematics
Languages : en
Pages : 374
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Book Description
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.
Author: Hiroshi Nagamochi
Publisher: Cambridge University Press
ISBN: 9781108735490
Category : Computers
Languages : en
Pages : 391
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Book Description
Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.
Author: Manuel Lladser
Publisher: American Mathematical Soc.
ISBN: 082184783X
Category : Mathematics
Languages : en
Pages : 251
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Book Description
This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.
Author: Martin Charles Golumbic
Publisher: Springer Science & Business Media
ISBN: 0387250360
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.
Author: Peter Jephson Cameron
Publisher: Cambridge University Press
ISBN: 9780521457613
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Author: Bruce A. Reed
Publisher: Springer Science & Business Media
ISBN: 0387224440
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research
