The Strange Logic of Random Graphs

Author: Joel Spencer
Publisher: Springer Science & Business Media
ISBN: 9783662045381
Release Date: 2013-03-09
Genre: Mathematics

The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

Introduction to Random Graphs

Author: Alan Frieze
Publisher: Cambridge University Press
ISBN: 9781107118508
Release Date: 2015-10-31
Genre: Mathematics

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Handbook of Graph Theory Second Edition

Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 9781439880197
Release Date: 2013-12-17
Genre: Mathematics

In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Mathematics and Computer Science III

Author: Michael Drmota
Publisher: Springer Science & Business Media
ISBN: 3764371285
Release Date: 2004-07-23
Genre: Computers

These are the Proceedings of the International Colloquium of Mathematics and Computer Science held at the Vienna University of Technology, September 13-17, 2004. This colloquium is the third one in a now regularly established series following the first two venues in September 2000 and September 2002 in Ver sailles. The present issue is centered around Combinatorics and Random Struc tures, Graph Theory, Analysis of Algorithms, Trees, Probability, Combinatorial Stochastic Processes, and Applications. It contains invited papers, contributed papers (lectures) and short communications (posters). The contributions have been carefully reviewed for their scientific quality and originality by the Scientific Committee chaired by Michael Drmota (Vienna Uni versity of Technology, Austria) and composed of Brigitte Chauvin (Universite de Versailles, France), Luc Devroye (McGill University, Canada), Daniele Gardy (Uni versite de Versailles, France), Philippe Flajolet (INRIA Rocquencourt, France), Michal Karonski (Adam Mickiewicz University, Poland), Abdelkader Mokkadem (Universite de Versailles, France), Helmut Prodinger (University of Witwatersrand, South Africa), J. Michael Steele (University of Pennsylvania, Philadelphia, USA), Brigitte Vallee (Universite de Caen, France). We thank them and all anonymous referees for their impressive work."

Exact Exponential Algorithms

Author: Fedor V. Fomin
Publisher: Springer Science & Business Media
ISBN: 3642165338
Release Date: 2010-10-26
Genre: Mathematics

For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

Topics in Discrete Mathematics

Author: Martin Klazar
Publisher: Springer Science & Business Media
ISBN: 9783540337003
Release Date: 2007-05-28
Genre: Mathematics

This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril. 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.

Geometric Discrepancy

Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 9783642039423
Release Date: 2009-12-02
Genre: Mathematics

What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.

The Algorithm Design Manual

Author: Steven S Skiena
Publisher: Springer Science & Business Media
ISBN: 9781848000704
Release Date: 2009-04-05
Genre: Computers

This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

The Simplex Method

Author: Karl Heinz Borgwardt
Publisher: Springer Science & Business Media
ISBN: 9783642615788
Release Date: 2012-12-06
Genre: Mathematics

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 method has caused a great fascination for many years. 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. One of these criteria is the average computation time, which amounts to an anal ysis of the average number of elementary arithmetic computations and of the number of pivot steps. A rigid analysis of the average behaviour may be very helpful for the decision which algorithm and which variant shall be used in practical applications. The subject and purpose of this book is to explain the great efficiency in prac tice by assuming certain distributions on the "real-world" -problems. Other stochastic models are realistic as well and so this analysis should be considered as one of many possibilities.

Information Theory Inference and Learning Algorithms

Author: David J. C. MacKay
Publisher: Cambridge University Press
ISBN: 0521642981
Release Date: 2003-09-25
Genre: Computers

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Combinatorics and Graph Theory

Author: John Harris
Publisher: Springer Science & Business Media
ISBN: 9780387797113
Release Date: 2009-04-03
Genre: Mathematics

These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Mobile Communication and Power Engineering

Author: Vinu Das
Publisher: Springer
ISBN: 9783642358647
Release Date: 2013-01-17
Genre: Computers

This book comprises the refereed proceedings of the International Conference, AIM/CCPE 2012, held in Bangalore, India, in April 2012. The papers presented were carefully reviewed and selected from numerous submissions and focus on the various aspects of research and development activities in computer science, information technology, computational engineering, mobile communication, control and instrumentation, communication system, power electronics and power engineering.

Newsletter

Author: New Zealand Mathematical Society
Publisher:
ISBN: UOM:39015057377932
Release Date: 2000
Genre: Mathematics


Foundations of Combinatorics with Applications

Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 9780486151502
Release Date: 2013-01-18
Genre: Mathematics

Suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics, this introductory text explores counting and listing, graphs, induction and recursion, and generating functions. Includes numerous exercises (some with solutions), notes, and references.