# Randomized Algorithms Approximation Generation and Counting

Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability.

Author: Russ Bubley

Publisher: Springer

ISBN: 9781447111801

Category: Computers

Page: 152

View: 985

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.

# Randomized Algorithms Approximation Generation and Counting

... a trivial example would be to pick a random permutation to transform the input to a sorting algorithm, say. Another significant use of sampling is in approximate counting, a problem which we go into in detail in the next chapter.

Author: Russ Bubley

Publisher: Springer Science & Business Media

ISBN: 1447106954

Category: Computers

Page: 152

View: 305

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.

# Randomized Algorithms

Author: Russ Howard Bubley

Publisher:

ISBN:

Category:

Page: 156

View: 526

# Mathematics and Computer Science III

Algorithms, Trees, Combinatorics and Probabilities Michael Drmota, Philippe Flajolet, Danièle Gardy, Bernhard Gittenberger. [4] R. Bubley, Randomized Algorithms: Approximation, Generation, and Counting, Springer-Verlag, New York, 2001.

Author: Michael Drmota

Publisher: Birkhäuser

ISBN: 3034879156

Category: Computers

Page: 556

View: 105

Mathematics and Computer Science III contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the Third International Colloquium on Mathematics and Computer Science, held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers.

# Surveys in Combinatorics 1999

[ 9 ] R. Bubley , Randomized algorithms : approximation , generation and counting , PhD thesis , University of Leeds , 1998 . ( 10 ) R. Bubley & M. Dyer , Path coupling : a technique for proving rapid mixing in Markov chains , in 38th ...

Author: J. D. Lamb

Publisher: Cambridge University Press

ISBN: 9780521653763

Category: Mathematics

Page: 298

View: 885

This volume, first published in 1999, is a valuable resource on combinatorics for graduate students and researchers.

# Fundamentals of Computation Theory

R. Bubley, Randomized algorithms: approximation, generation and counting, Springer-Verlag, London, 2001. R. Bubley and M. Dyer, Graph orientations with no sink and an approximation for a hard case of #SAT, in Proc.

Author: Maciej Liskiewicz

Publisher: Springer Science & Business Media

ISBN: 3540281932

Category: Computers

Page: 576

View: 769

This book constitutes the refereed proceedings of the 15th International Symposium Fundamentals of Computation Theory, FCT 2005, held in Lübeck, Germany in August 2005. The 46 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on circuits, automata, complexity, approximability, computational and structural complexity, graphs and complexity, computational game theory, visual cryptography and computational geometry, query complexity, distributed systems, automata and formal languages, semantics, approximation algorithms, average case complexity, algorithms, graph algorithms, and pattern matching.

# Algorithms for Random Generation and Counting A Markov Chain Approach

Other recent progress on counting and generating graphs with given degrees, using very different methods, can be found in ... in the design of an improved randomised approximation algorithm for the permanent of an arbitrary 0-1 matrix.

Author: A. Sinclair

Publisher: Springer Science & Business Media

ISBN: 1461203236

Category: Computers

Page: 147

View: 418

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.

# Combinatorial and Algorithmic Aspects of Networking

ACM, New York (1997) Roth, D.: On the hardness of approximate reasoning. Artificial Intelligence 82, 273–302 (1996) Russ, B.: Randomized Algorithms: Approximation, Generation, and Counting, Distinguished dissertations.

Author: Pawel Pralat

Publisher: Springer

ISBN: 3540772944

Category: Computers

Page: 152

View: 558

This book constitutes the thoroughly refereed post-conference proceedings of the 4th Workshop on Combinatorial and Algorithmic Aspects of Networking, CAAN 2007, held in Halifax, Canada, in August 2007, co-located with the 10th Workshop on Algorithms and Data Structures, WADS 2007. The main focus is on strategies for searching in networks, and for cleaning networks of unwanted intruders, on different routing strategies, and on scheduling and load balancing.

# Pattern Recognition

Springer, Heidelberg (2005). https://doi.org/10.1007/1160468638 6. Roth, D.: On the hardness of approximate reasoning. Artif. Intell. 82(1), 273–302 (1996) 7. Russ, B.: Randomized Algorithms: Approximation. Generation, and Counting.

Author: Karina Mariela Figueroa Mora

Publisher: Springer Nature

ISBN: 3030490769

Category: Computers

Page: 342

View: 693

This book constitutes the proceedings of the 12th Mexican Conference on Pattern Recognition, MCPR 2020, which was due to be held in Morelia, Mexico, in June 2020. The conference was held virtually due to the COVID-19 pandemic. The 31 papers presented in this volume were carefully reviewed and selected from 67 submissions. They were organized in the following topical sections: pattern recognition techniques; image processing and analysis; computer vision; industrial and medical applications of pattern recognition; natural language processing and recognition; artificial intelligence techniques and recognition.

# Advances in Artificial Intelligence and Soft Computing

Russ, B.: Randomized Algorithms: Approximation, Generation, and Counting. Distingished Dissertations. Springer, Heidelberg (2001) 4. Zmazek, B.: Estimating the traffic on weighted cactus networks in linear time.

Author: Grigori Sidorov

Publisher: Springer

ISBN: 3319270605

Category: Computers

Page: 575

View: 371

The two volume set LNAI 9413 + LNAI 9414 constitutes the proceedings of the 14th Mexican International Conference on Artificial Intelligence, MICAI 2015, held in Cuernavaca, Morelos, Mexico, in October 2015. The total of 98 papers presented in these proceedings was carefully reviewed and selected from 297 submissions. They were organized in topical sections named: natural language processing; logic and multi-agent systems; bioinspired algorithms; neural networks; evolutionary algorithms; fuzzy logic; machine learning and data mining; natural language processing applications; educational applications; biomedical applications; image processing and computer vision; search and optimization; forecasting; and intelligent applications.