Also the present second edition of this book is an introduction to the theory of clas- sification, enumeration, construction and generation of finite unlabeled structures in mathematics and sciences. Since the publication of the first edition in 1991 the constructive theory of un- labeled finite structures has made remarkable progress. For example, the first- designs with moderate parameters were constructed, in Bayreuth, by the end of 1994 ( 9]). The crucial steps were - the prescription of a suitable group of automorphisms, i. e. a stabilizer, and the corresponding use of Kramer-Mesner...
Also the present second edition of this book is an introduction to the theory of clas- sification, enumeration, construction and generation of finite ...
I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which - not exactly contrary to my personal expectations - has apparently been accepted reasonably weIl by the global optimization community. My objective in putting this book together was originally - and still is - to detail the major algorithmic ideas in linear optimization that have evolved in the past fifty years or so and that have changed the historical optimization "landscape" in substantial ways - both theoretically and computationally....
I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which...
Leave nothing to chance. This cliche embodies the common belief that ran- domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba- bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time,...
Leave nothing to chance. This cliche embodies the common belief that ran- domness has no place in carefully planned methodologies, every step should b...
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...
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 th...
For more than 35 years now, George B. Dantzig's Simplex-Method has been the most efficient mathematical tool for solving linear programming problems. It is proba- bly that mathematical algorithm for which the most computation time on computers is spent. This fact explains the great interest of experts and of the public to understand the method and its efficiency. But there are linear programming problems which will not be solved by a given variant of the Simplex-Method in an acceptable time. The discrepancy between this (negative) theoretical result and the good practical behaviour of the...
For more than 35 years now, George B. Dantzig's Simplex-Method has been the most efficient mathematical tool for solving linear programming problems. ...
Now fully updated in a third edition, this is a comprehensive textbook on combinatorial optimization. It puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete but concise proofs, also for many deep results, some of which have not appeared in print before. Recent topics are covered as well, and numerous references are provided. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new...
Now fully updated in a third edition, this is a comprehensive textbook on combinatorial optimization. It puts special emphasis on theoretical resul...
This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nesetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.
This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jar...
With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the underlying mathematical object, and properties exploited by algorithms are often closely tied to classical structural analysis in mathematics. This connection between algorithms and structure is in particular apparent in discrete mathematics, where proofs are often constructive, and can be turned into algorithms more directly. The principle of greediness plays a fundamental role both in the design of continuous algorithms (where it is called the...
With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the unde...
This is the first comprehensive exposition of basic lower-bounds arguments, reviewing gems discovered in the past two decades right up to results from the last year. Covers a wide spectrum of models: circuits, formulas, communication protocols, branching programs.
This is the first comprehensive exposition of basic lower-bounds arguments, reviewing gems discovered in the past two decades right up to results from...
I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen- eral tools that can be learned and then applied, to various problems. Matroid theory is...
I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization...
