Probabilistic Methods for Algorithmic Discrete Mathematics (Algorithms and Combinatorics)

Book Description

The book gives an accessible account of modern probabilistic methods for analyzing combinatorial structures and algorithms. It will be an useful guide for graduate students and researchers.
Special features included: a simple treatment of Talagrand's inequalities and their applications; an overview and many carefully worked out examples of the probabilistic analysis of combinatorial algorithms; a discussion of the "exact simulation" algorithm (in the context of Markov Chain Monte Carlo Methods); a general method for finding asymptotically optimal or near optimal graph colouring, showing how the probabilistic method may be fine-tuned to exploit the structure of the underlying graph; a succinct treatment of randomized algorithms and derandomization techniques.

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Intersting Studies Hampered by LEDA and LP Dependencies

Algorithms on Trees and Graphs
Gabriel Valiente
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540435506

Book Description

Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, like approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms. Numerous illustrations, examples, and exercises, and a comprehensive bibliography support students and professionals in using the book as a text and source of reference

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Intersting Studies Hampered by LEDA and LP Dependencies.......2003-12-24

I'm pleased with the text in this book; the descriptions are almost all clear, and reading through the book gives me insight into some more interesting problems in trees and graphs. The high points of the book are its treaments of tree and graph isomorphism, but I also found the discussions of non-traditional traversal algorithms on trees and graphs very interesting. The author discussions leaf-first, breadth-first, and depth-first traversals and provides algorithms for their implementation. Many of the algorithms include correctness proofs.

These topics alone made the book worth its to me. A deep academic book that costs less than $50 is nearly unheared-of.

Unfortunately, there are two flaws that make the book hard to use. In a nutshell, the author expects the reader to buy into a couple of pretty invasive and expensive propositions.

First, the author decided to use literate programming for all of his presented algorithms and code fragments. This isn't so bad, since literate programming is about documenting code. If you suppose that the author wrote the code, then documented it, then calld it a book, using a tool like literate programming seems like a natural choice.

But if you're not familiar with literate programming, it's a bit of a chore. The author's introduction to literate programming doesn't help with some of the questions even an experienced programmer might have wend reading the text. More practically, literate programming enforces operators that are different than most C/C++ developers are familiar with, and can cause confusion when reading the text. ^ is used, for example, to indicate a logical and, where C/C++ developers expect it to indicate a bitwise-exclusive or.

While it's esay to eventually overcome such tricks of memory, I've been finding it hard to scan literate programs to find definitions and declarations. The author doesn't include a CD (and at this cover price, that is hard to fault) but also doesn't make his code available for download. His website includes a LEDA-based program that interactively demonstrates some algorithms, but doesn't include code for the algorithm his own books develops and discusses.

The other decision made by the author, to the overwhelming inconvenience of this reader, is the reliance on the LEDA library for his samples and programs. The algorithms are understandable without the library, but a reader without access to LEDA doesn't benefit from any of the visualizations the author provides. , and several include

In fact, the author spends about 40 pages discussing LEDA and the characteristics of its implementation. Maybe researchers working on tree and graph algorithms all use LEDA and have ready access to it, but the literate programming code provided to for some of the algorithms isn't useful to readers who aren't familiar with LEDA, as researching the definitions and declarations themsleves becomes arduous.

The bibliography is very diverse, with more than 380 entries and is well-cited throughout the book. Unfortunately, the author sometimes relies on the bibliography too much. On page 392, the author brings up "the so-called graph isopomorphism disease" without defining it himself; he instead relies on his bibliography entries to give the user any definition or background on the "disease".

Unfortunately, the index received not nearly as much attention as the bibliography; neglecting whitespace, it's scarcely more than a single page long!

The book appears to be something more than a research paper, but is written much like a research apper would be. The book probably also serves well for a class that teaches this subject, and assumes LEDA and literate programming as prerequisites. But as a commercial developer who's interested in applying advanced graph and tree algorithms to the work I'm doing, I found the book has limited its value by relying on LEDA and applying literate programming.

Book Description

This book constitutes the thoroughly refereed post-proceedings of the 7th International Symposium on Graph Drawing, GD '99, held in Stirin Castle, Czech Republic, in September 1999.The 38 revised full papers presented together with three invited contributions, two posters, and a report on the graph drawing contest were carefully reviewed and selected from 59 submissions. Among the topics addressed are orthogonality, levels, clusters, drawing, planarity, applications, symmetry, representations, and proximity and trees.

An Algorithmic Theory of Numbers, Graphs and Convexity (CBMS-NSF Regional Conference Series in Applied Mathematics)

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An Algorithmic Theory of Numbers, Graphs and Convexity (CBMS-NSF Regional Conference Series in Applied Mathematics)
Laszlo Lovasz
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898712033

Book Description

A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous diophantine approximation method. Although both were developed to study, on a theoretical level, the feasibility of computing some specialized problems in polynomial time, they appear to have practical applications. The book first describes use of the simultaneous diophantine method to develop sophisticated rounding procedures. Then a model is described to compute upper and lower bounds on various measures of convex bodies. Use of the two algorithms is brought together by the author in a study of polyhedra with rational vertices. The book closes with some applications of the results to combinatorial optimization.

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Algorithmic Graph Theory
Alan Gibbons
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521288819

Book Description

This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and their complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms.

A number of exercises and outlines of solutions are included to extend and motivate the material of the text.

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This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms. A number of exercises and outlines of solutions are included to extend and motivate the material of the text.

Advances in Computer Games: 11th International Conference, ACG 2005, Taipei, Taiwan, September 6-8, 2005. Revised Papers (Lecture Notes in Computer Science)

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Advances in Computer Games: 11th International Conference, ACG 2005, Taipei, Taiwan, September 6-8, 2005. Revised Papers (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

This book constitutes the thoroughly refereed post-proceedings of the 11th International Conference on Advances in Computer Games, ACG 2005, held in Taipei, Taiwan, in September 2005 in conjunction with the 10th Computer Olympiad.

The 20 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 32 submissions. The papers cover all aspects of artificial intelligence in computer-game playing. Reasearch topics addressed are automatic generation, optimization, opponent modelling, search, knowledge representation, and graph history interaction. Games covered are western chess, chinese and japanese chess, checkers, lose checkers, amazons, go, poker, loa, mastermind, awari, ataxx, pool, as well as the two theoretical games connect and sumbers.

Algorithm Theory - SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006, Proceedings (Lecture Notes in Computer Science)

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Algorithm Theory - SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006, Proceedings (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 354035753X

Book Description

This book constitutes the refereed proceedings of the 10th Scandinavian Workshop on Algorithm Theory, SWAT 2006, held in Riga, Latvia, in July 2006.

The 36 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 154 submissions. The papers address all issues of theoretical algorithmics and applications in various fields including graph algorithms, computational geometry, scheduling, approximation algorithms, network algorithms, data storage and manipulation, combinatorics, sorting, searching, online algorithms, optimization, etc.

Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006, Proceedings (Lecture Notes in Computer Science)

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Algorithmic Aspects in Information and Management: Second International Conference, AAIM 2006, Hong Kong, China, June 20-22, 2006, Proceedings (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

This book constitutes the refereed proceedings of the Second International Conference on Algorithmic Aspects in Information and Management, AAIM 2006, held in Hong Kong, China in June 2006.

The 34 revised full papers presented together with abstracts of 2 invited talks were carefully reviewed and selected from 263 submissions. The papers cover topics from areas such as online scheduling, game and finance, data structures and algorithms, computational geometry, optimization, graph, and string.

Algorithmic Aspects in Information and Management: Third International Conference, AAIM 2007, Portland, OR, USA, June 6-8, 2007, Proceedings (Lecture Notes in Computer Science)

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Algorithmic Aspects in Information and Management: Third International Conference, AAIM 2007, Portland, OR, USA, June 6-8, 2007, Proceedings (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540728686

Book Description

This book constitutes the refereed proceedings of the Third International Conference on Algorithmic Aspects in Information and Management, AAIM 2007, held in Portland, OR, USA in June 2007.

The 39 revised full papers presented together with abstracts of 3 invited talks were carefully reviewed and selected from 120 submissions. The papers are organized in topical sections on graph algorithms, combinatorics, scheduling, graph theory, network algorithms, game theory, option theory, computational geometry, graph theory and combinatorics, as well as networks and data.

Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)

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Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
Francine Blanchet-Sadri
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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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 into this emerging research area, Algorithmic Combinatorics on Partial Words presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores up-and-coming techniques for solving partial word problems as well as the future direction of research. This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered partial words while the following section introduces some important properties of pcodes, details a variety of ways of defining and analyzing pcodes, and shows that the pcode property is decidable using two different techniques. In the final part, the author solves various equations on partial words, presents binary and ternary correlations, and covers unavoidable sets of partial words. Setting the tone for future research in this field, this book lucidly develops the central ideas and results of combinatorics on partial words.

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