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Author: Russ Bubley
Publisher: Springer Science & Business Media
ISBN: 1447106954
Category : Computers
Languages : en
Pages : 167
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Book Description
Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.
Author: Russ Bubley
Publisher: Springer Science & Business Media
ISBN: 1447106954
Category : Computers
Languages : en
Pages : 167
Get Book Here
Book Description
Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.
Author: A. Sinclair
Publisher: Springer Science & Business Media
ISBN: 0817636587
Category : Computers
Languages : en
Pages : 161
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Book Description
This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.
Author: A. Sinclair
Publisher: Springer Science & Business Media
ISBN: 1461203236
Category : Computers
Languages : en
Pages : 156
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Book Description
This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.
Author: Jacques Fleuriot
Publisher: Springer Science & Business Media
ISBN: 085729329X
Category : Mathematics
Languages : en
Pages : 150
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Book Description
Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague. In A Combination of Geometry Theorem Proving and Nonstandard Analysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.
Author: Eamonn O'Neill
Publisher: Springer Science & Business Media
ISBN: 1447103556
Category : Computers
Languages : en
Pages : 324
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Book Description
The topic of the research reported here is direct user participation in the task-based development of interactive software systems. Building usable software demands understanding and supporting users and their tasks. Users are a primary source of usability requirements and knowledge, since users can be expected to have intimate and extensive knowledge of themselves, their tasks and their working environment. Task analysis approaches to software development encourage a focus on supporting users and their tasks while participatory design approaches encourage users' direct, active contributions to software development work. However, participatory design approaches often concentrate their efforts on design activities rather than on wider system development activities, while task analysis approaches generally lack active user participation beyond initial data gathering. This research attempts an integration of the strengths of task analysis and user participation within an overall software development process. This work also presents detailed empirical and theoretical analyses of what it is for users and developers to cooperate, of the nature of user-developer interaction in participatory settings. Furthermore, it makes operational and assesses the effectiveness of user participation in development and the impact of user-developer cooperation on the resulting software product. The research addressed these issues through the development and application of an approach to task based participatory development in two real world development projects. In this integrated approach, the respective strengths of task analysis and participatory design methods complemented each other's weaker aspects.
Author: Tracy A. Gardner
Publisher: Springer Science & Business Media
ISBN: 1447101219
Category : Computers
Languages : en
Pages : 211
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Book Description
Object-oriented inheritance has been in widespread use for a decade, and it is now realised that although inheritance is a powerful modelling tool with many associated advantages, its benefits are not automatically conferred on systems that simply use it. This book introduces a model of inheritance based around five fundamental inheritance relationships. Each relationship has a clear conceptual basis, representing a fundamental, specialised use of inheritance. The resulting model replaces a confused notion of inheritance with five distinct conceptual relationships supporting more precise modelling of systems and capturing the semantic intent of each use of inheritance within a system.
Author: Rajeev Motwani
Publisher: Cambridge University Press
ISBN: 9780521474658
Category : Computers
Languages : en
Pages : 496
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Book Description
This book presents basic tools from probability theory used in algorithmic applications, with concrete examples.
Author: Klaus Jansen
Publisher: Springer
ISBN: 354044436X
Category : Computers
Languages : en
Pages : 290
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Book Description
This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.
Author: Mikhail J. Atallah
Publisher: CRC Press
ISBN: 9781420049503
Category : Computers
Languages : en
Pages : 1328
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Book Description
Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Author: Sanjeev Arora
Publisher: Springer Science & Business Media
ISBN: 3540407707
Category : Computers
Languages : en
Pages : 418
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Book Description
This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.
