Algorithms For Random Generation And Counting A Markov Chain Approach

Author : A. Sinclair
Publisher : Springer Science & Business Media
ISBN 13 : 1461203236
Total Pages : 156 pages
Book Rating : 4.30/5 ( download)

DOWNLOAD NOW!

Download or read book Algorithms for Random Generation and Counting: A Markov Chain Approach written by A. Sinclair and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alistair Sinclair
Publisher :
ISBN 13 : 9783764336585
Total Pages : 146 pages
Book Rating : 4.87/5 ( download)

DOWNLOAD NOW!

Download or read book Algorithms for Random Generation and Counting written by Alistair Sinclair and published by . This book was released on 1993 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Russ Bubley
Publisher : Springer Science & Business Media
ISBN 13 : 1447106954
Total Pages : 167 pages
Book Rating : 4.51/5 ( download)

DOWNLOAD NOW!

Download or read book Randomized Algorithms: Approximation, Generation, and Counting written by Russ Bubley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Olle Häggström
Publisher : Cambridge University Press
ISBN 13 : 9780521890014
Total Pages : 132 pages
Book Rating : 4.12/5 ( download)

DOWNLOAD NOW!

Download or read book Finite Markov Chains and Algorithmic Applications written by Olle Häggström and published by Cambridge University Press. This book was released on 2002-05-30 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

Author : Mark Jerrum
Publisher : Birkhäuser
ISBN 13 : 3034880057
Total Pages : 112 pages
Book Rating : 4.53/5 ( download)

DOWNLOAD NOW!

Download or read book Counting, Sampling and Integrating: Algorithms and Complexity written by Mark Jerrum and published by Birkhäuser. This book was released on 2012-12-06 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.

Author : Michel Habib
Publisher : Springer Science & Business Media
ISBN 13 : 3662127881
Total Pages : 342 pages
Book Rating : 4.89/5 ( download)

DOWNLOAD NOW!

Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

Author : Zhipeng Cai
Publisher : Springer
ISBN 13 : 3319087835
Total Pages : 704 pages
Book Rating : 4.32/5 ( download)

DOWNLOAD NOW!

Download or read book Computing and Combinatorics written by Zhipeng Cai and published by Springer. This book was released on 2014-07-05 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Computing and Combinatorics, COCOON 2014, held in Atlanta, GA, USA, in August 2014. The 51 revised full papers presented were carefully reviewed and selected from 110 submissions. There was a co-organized workshop on computational social networks (CSoNet 2014) where 8 papers were accepted. The papers cover the following topics: sampling and randomized methods; logic, algebra and automata; database and data structures; parameterized complexity and algorithms; computational complexity; computational biology and computational geometry; approximation algorithm; graph theory and algorithms; game theory and cryptography; scheduling algorithms and circuit complexity and CSoNet.

Author : Panos M. Pardalos
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870877
Total Pages : 350 pages
Book Rating : 4.74/5 ( download)

DOWNLOAD NOW!

Download or read book Randomization Methods in Algorithm Design written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on proceedings held during the DIMACS workshop on Randomization Methods in Algorithm Design in December 1997 at Princeton. The workshop was part of the DIMACS Special Year on Discrete Probability. It served as an interdisciplinary research workshop that brought together a mix of leading theorists, algorithmists and practitioners working in the theory and implementation aspects of algorithms involving randomization. Randomization has played an important role in the design of both sequential and parallel algorithms. The last decade has witnessed tremendous growth in the area of randomized algorithms. During this period, randomized algorithms went from being a tool in computational number theory to finding widespread applications in many problem domains. Major topics covered include randomization techniques for linear and integer programming problems, randomization in the design of approximate algorithms for combinatorial problems, randomization in parallel and distributed algorithms, practical implementation of randomized algorithms, de-randomization issues, and pseudo-random generators. This volume focuses on theory and implementation aspects of algorithms involving randomization. It would be suitable as a graduate or advanced graduate text.

Author : Istvan Miklos
Publisher : CRC Press
ISBN 13 : 1351971611
Total Pages : 390 pages
Book Rating : 4.14/5 ( download)

DOWNLOAD NOW!

Download or read book Computational Complexity of Counting and Sampling written by Istvan Miklos and published by CRC Press. This book was released on 2019-02-21 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared toward researchers in enumerative combinatorics, discrete mathematics, and theoretical computer science. The book covers the following topics: Counting and sampling problems that are solvable in polynomial running time, including holographic algorithms; #P-complete counting problems; and approximation algorithms for counting and sampling. First, it opens with the basics, such as the theoretical computer science background and dynamic programming algorithms. Later, the book expands its scope to focus on advanced topics, like stochastic approximations of counting discrete mathematical objects and holographic algorithms. After finishing the book, readers will agree that the subject is well covered, as the book starts with the basics and gradually explores the more complex aspects of the topic. Features: Each chapter includes exercises and solutions Ideally written for researchers and scientists Covers all aspects of the topic, beginning with a solid introduction, before shifting to computational complexity’s more advanced features, with a focus on counting and sampling

Author : Rajeev Motwani
Publisher : Cambridge University Press
ISBN 13 : 1139643134
Total Pages : 496 pages
Book Rating : 4.39/5 ( download)

DOWNLOAD NOW!

Download or read book Randomized Algorithms written by Rajeev Motwani and published by Cambridge University Press. This book was released on 1995-08-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.