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Greedoids

by B. (University Of Bonn, Germany) Korte, L. (University Of Budapest, Hungary) Lovasz e R. (University Of Bonn, Germany) Schrader

108,14€ + 10% CARD

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 This monograph attempts to unify different mathematical approaches and to lead the reader from fundamental results in matroid theory to the current state-of-the-art in open research problems. It reviews classical concepts from matroid theory and extends them to greedoids ("greedy" algorithms).
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Combinatorial Optimization - Theory And Algorithms

by Bernhard Korte e Jens Vygen

79,49€ + 10% CARD

 This comprehensive textbook on combinatorial optimization emphasizes theoretical results and algorithms with provably good performance, in contrast to heuristics. The text contains complete but concise proofs, and also provides numerous exercises and references.
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Optimal Interconnection Trees In The Plane - Theory, Algorithms And Applications

by Marcus Brazil e Martin Zachariasen

59,61€ + 10% CARD

 The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane.
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Combinatorics And Complexity Of Partition Functions

by Alexander Barvinok

145,09€ + 10% CARD

 <p>Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. </p><p>The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. </p>
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Geometric Discrepancy - An Illustrated Guide

171,59€ + 10% CARD

 Discrepancy theory is also called the theory of irregularities of distribution. There are subfields closely connected to the original numberÂ theoretic roots of discrepancy theory, areas related to Ramsey theory and to hypergraphs, and also results supporting eminently practical methods and algorithms for numerical integration and similar tasks.
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Matrices And Matroids For Systems Analysis

by Kazuo Murota

158,34€ + 10% CARD

 A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers an introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis.
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Graph Colouring And The Probabilistic Method

by Bruce Reed e Michael Molloy

158,34€ + 10% CARD

 Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.
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Geometry Of Cuts And Metrics

by Michel Marie Deza e Monique Laurent

171,59€ + 10% CARD

 Cuts are well-known objects in graph theory, combinatorics, and combinatorial optimization and, perhaps less well-known, in analysis and probability theory. Featuring a rigorous use of cut polyhedra, this book summarizes various results in all these areas in a unified way, and points out unnoticed relations between diverse results in these fields.
ENGLISH

Combinatorial Optimization - Theory And Algorithms

by Bernhard Korte e Jens Vygen

78,16€ + 10% CARD

 This comprehensive textbook on combinatorial optimization emphasizes theoretical results and algorithms with provably good performance, in contrast to heuristics. The text contains complete but concise proofs, and also provides numerous exercises and references.
ENGLISH

Boolean Function Complexity - Advances And Frontiers

by Stasys Jukna

92,74€ + 10% CARD

 Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science.
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Sparsity - Graphs, Structures, And Algorithms

by Jaroslav Nesetril e Patrice Ossona De Mendez

104,68€ + 10% CARD

 This book offers a systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is typical of a fuzzy notion, the authors present a unifying classification of general classes of structures.
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Discrete Images, Objects, And Functions In Zn

by Klaus Voss

118,59€ + 10% CARD

 Voss' book which deals with theoretical problems of digital image processing is an indispensable source of information for all those who are involved in the design, implementation, and application of mathematically sound algorithms in image processing; it is written for engineers, mathematicians, and computer scientists. The author, who is a well-known expert in the field of digital image processing, presents important new research which generalizes the currently used two-dimensional theory to n dimensions.
ENGLISH

Discrete And Computational Geometry - The Goodman-Pollack Festschrift

171,59€ + 10% CARD

 With contributions by numerous experts
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New Trends In Discrete And Computational Geometry

59,61€ + 10% CARD

 In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms.
ENGLISH

Mathematics Of Paul Erdos Ii

95,40€ + 10% CARD

 In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin guished group of researchers with interests spanning a variety of fields related to Erdos'' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos'' career to solicit a col lection of articles illustrating various aspects of Erdos'' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos'' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap ter includes an introduction which often presents a sample of related Erdos'' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos'' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.
ENGLISH

Mathematics Of Paul Erdos I

95,40€ + 10% CARD

 In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin guished group of researchers with interests spanning a variety of fields related to Erdos'' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos'' career to solicit a col lection of articles illustrating various aspects of Erdos'' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos'' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap ter includes an introduction which often presents a sample of related ErdOs'' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos'' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.
ENGLISH

Irregularities Of Partitions

59,61€ + 10% CARD

 The problem of uniform distribution of sequences initiated by Hardy, Little wood and Weyl in the 1910''s has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.
ENGLISH

Simplex Method - A Probabilistic Analysis

by Karl Heinz Borgwardt

59,61€ + 10% CARD

 While the "worst-case analysis" of some variants of the method shows that this is not a "good" algorithm in the usual sense of complexity theory, it seems to be useful to apply other criteria for a judgement concerning the quality of the algorithm.
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Systems Analysis By Graphs And Matroids - Structural Solvability And Controllability

by Kazuo Murota

118,59€ + 10% CARD

 Illustrates how engineering problems can be solved using the results of combinatorial mathematics through mathematical modelling. It covers the structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant system.
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Mathematics Of Ramsey Theory

118,59€ + 10% CARD

 One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.
ENGLISH

Geometric Algorithms And Combinatorial Optimization

by Alexander Schrijver, Laszlo Lovasz e Martin Grotschel

158,34€ + 10% CARD

 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.
ENGLISH

Geometric Algorithms And Combinatorial Optimization

by Alexander Schrijver, Laszlo Lovasz e Martin Grotschel

95,40€ + 10% CARD

 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.
ENGLISH

Strange Logic Of Random Graphs

by Joel Spencer

118,59€ + 10% CARD

 This book joins the study of random graphs with mathematical logic. The possible threshold phenomena are studied for all statements expressible in a given language. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.
ENGLISH

Applied Finite Group Actions

by Adalbert Kerber

171,59€ + 10% CARD

 The topic of this book is finite group actions and their use in order to approach finite unlabelled structures by defining them as orbits of finite groups of sets. Well-known examples are graph, linear codes, chemical isomers, spin configurations, and isomorphism classes of combinatorial designs.
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