Probabilistic Analysis Of Some Search Algorithms

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Probabilistic Analysis of Algorithms

Author : Micha Hofri
Publisher : Springer Science & Business Media
ISBN 13 : 1461248000
Total Pages : 254 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Probabilistic Analysis of Algorithms by : Micha Hofri

Download or read book Probabilistic Analysis of Algorithms written by Micha Hofri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Analysis of Algorithms begins with a presentation of the "tools of the trade" currently used in probabilistic analyses, and continues with an applications section in which these tools are used in the analysis ofr selected algorithms. The tools section of the book provides the reader with an arsenal of analytic and numeric computing methods which are then applied to several groups of algorithms to analyze their running time or storage requirements characteristics. Topics covered in the applications section include sorting, communications network protocols and bin packing. While the discussion of the various algorithms is sufficient to motivate their structure, the emphasis throughout is on the probabilistic estimation of their operation under distributional assumptions on their input. Probabilistic Analysis of Algorithms assumes a working knowledge of engineering mathematics, drawing on real and complex analysis, combinatorics and probability theory. While the book is intended primarily as a text for the upper undergraduate and graduate student levels, it contains a wealth of material and should also prove an important reference for researchers. As such it is addressed to computer scientists, mathematicians, operations researchers, and electrical and industrial engineers who are interested in evaluating the probable operation of algorithms, rather than their worst-case behavior.

Probability and Computing

Author : Michael Mitzenmacher
Publisher : Cambridge University Press
ISBN 13 : 9780521835404
Total Pages : 372 pages
Book Rating : 4.8/5 (354 download)

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Book Synopsis Probability and Computing by : Michael Mitzenmacher

Download or read book Probability and Computing written by Michael Mitzenmacher and published by Cambridge University Press. This book was released on 2005-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

The Simplex Method

Author : Karl Heinz Borgwardt
Publisher : Springer Science & Business Media
ISBN 13 : 3642615783
Total Pages : 279 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis The Simplex Method by : Karl Heinz Borgwardt

Download or read book The Simplex Method written by Karl Heinz Borgwardt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probabilistic Methods for Algorithmic Discrete Mathematics

Author : Michel Habib
Publisher : Springer Science & Business Media
ISBN 13 : 3662127881
Total Pages : 342 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib

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.

The Probabilistic Method

Author : Noga Alon
Publisher : John Wiley & Sons
ISBN 13 : 1119062071
Total Pages : 396 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis The Probabilistic Method by : Noga Alon

Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

Probability Theory and Combinatorial Optimization

Author : J. Michael Steele
Publisher : SIAM
ISBN 13 : 9781611970029
Total Pages : 168 pages
Book Rating : 4.9/5 (7 download)

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Book Synopsis Probability Theory and Combinatorial Optimization by : J. Michael Steele

Download or read book Probability Theory and Combinatorial Optimization written by J. Michael Steele and published by SIAM. This book was released on 1997-01-01 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. There are three fundamental probabilistic themes that are examined through our concrete investigations. First, there is a systematic exploitation of martingales. The second theme that is explored is the systematic use of subadditivity of several flavors, ranging from the naïve subadditivity of real sequences to the subtler subadditivity of stochastic processes. The third and deepest theme developed here concerns the application of Talagrand's isoperimetric theory of concentration inequalities.

Average Case Analysis of Algorithms on Sequences

Author : Wojciech Szpankowski
Publisher : John Wiley & Sons
ISBN 13 : 1118031024
Total Pages : 580 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Average Case Analysis of Algorithms on Sequences by : Wojciech Szpankowski

Download or read book Average Case Analysis of Algorithms on Sequences written by Wojciech Szpankowski and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely book on a topic that has witnessed a surge of interest over the last decade, owing in part to several novel applications, most notably in data compression and computational molecular biology. It describes methods employed in average case analysis of algorithms, combining both analytical and probabilistic tools in a single volume. * Tools are illustrated through problems on words with applications to molecular biology, data compression, security, and pattern matching. * Includes chapters on algorithms and data structures on words, probabilistic and analytical models, inclusion-exclusion principles, first and second moment methods, subadditive ergodic theorem and large deviations, elements of information theory, generating functions, complex asymptotic methods, Mellin transform and its applications, and analytic poissonization and depoissonization. * Written by an established researcher with a strong international reputation in the field.

Analysis and Design of Algorithms for Combinatorial Problems

Author : G. Ausiello
Publisher : Elsevier
ISBN 13 : 0080872204
Total Pages : 335 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Analysis and Design of Algorithms for Combinatorial Problems by : G. Ausiello

Download or read book Analysis and Design of Algorithms for Combinatorial Problems written by G. Ausiello and published by Elsevier. This book was released on 1985-05-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed.The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.

The Traveling Salesman Problem and Its Variations

Author : G. Gutin
Publisher : Springer Science & Business Media
ISBN 13 : 1402006640
Total Pages : 837 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Traveling Salesman Problem and Its Variations by : G. Gutin

Download or read book The Traveling Salesman Problem and Its Variations written by G. Gutin and published by Springer Science & Business Media. This book was released on 2002-05-31 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant treatment of a knotty problem in computing. This volume contains chapters written by reputable researchers and provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, and includes a thorough computational analysis of heuristic and metaheuristic algorithms.

Randomized Algorithms

Author : Rajeev Motwani
Publisher : Cambridge University Press
ISBN 13 : 1139643134
Total Pages : 496 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis Randomized Algorithms by : Rajeev Motwani

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.

An Annotated Timeline of Operations Research

Author : Saul I. Gass
Publisher : Springer Science & Business Media
ISBN 13 : 9781402081125
Total Pages : 240 pages
Book Rating : 4.0/5 (811 download)

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Book Synopsis An Annotated Timeline of Operations Research by : Saul I. Gass

Download or read book An Annotated Timeline of Operations Research written by Saul I. Gass and published by Springer Science & Business Media. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising from the urgent operational issues of World War II, the philosophy and methodology of Operations Research (OR) has permeated the resolution of decision problems in business, industry, and government. This work recounts the evolution of OR as the science of decision making. It chronicles the history of OR in the form of expository entries.

Algorithms and Theory of Computation Handbook

Author : Mikhail J. Atallah
Publisher : CRC Press
ISBN 13 : 9781420049503
Total Pages : 1328 pages
Book Rating : 4.0/5 (495 download)

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Book Synopsis Algorithms and Theory of Computation Handbook by : Mikhail J. Atallah

Download or read book Algorithms and Theory of Computation Handbook written by Mikhail J. Atallah and published by CRC Press. This book was released on 1998-11-23 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Integer Programming and Related Areas A Classified Bibliography 1976–1978

Author : D. Hausmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642463835
Total Pages : 326 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Integer Programming and Related Areas A Classified Bibliography 1976–1978 by : D. Hausmann

Download or read book Integer Programming and Related Areas A Classified Bibliography 1976–1978 written by D. Hausmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integer and Combinatorial Optimization

Author : Laurence A. Wolsey
Publisher : John Wiley & Sons
ISBN 13 : 1118626869
Total Pages : 782 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Integer and Combinatorial Optimization by : Laurence A. Wolsey

Download or read book Integer and Combinatorial Optimization written by Laurence A. Wolsey and published by John Wiley & Sons. This book was released on 2014-08-28 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.

Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

Author :
Publisher : SIAM
ISBN 13 : 9780898713138
Total Pages : 532 pages
Book Rating : 4.7/5 (131 download)

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Book Synopsis Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms by :

Download or read book Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms written by and published by SIAM. This book was released on 1993-01-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Proceedings of a conference that took place in Austin, Texas in January 1993. Contributors are impressive names from the field of computer science, including Donald Knuth, author of several computer books of "biblical" importance. The diverse selection of paper topics includes dynamic point location, ray shooting, and the shortest paths in planar maps; optimistic sorting and information theoretic complexity; and an optimal randomized algorithm for the cow-path problem. No index. Annotation copyright by Book News, Inc., Portland, OR.

An Introduction to the Analysis of Algorithms

Author : Robert Sedgewick
Publisher : Addison-Wesley
ISBN 13 : 0133373487
Total Pages : 735 pages
Book Rating : 4.1/5 (333 download)

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Book Synopsis An Introduction to the Analysis of Algorithms by : Robert Sedgewick

Download or read book An Introduction to the Analysis of Algorithms written by Robert Sedgewick and published by Addison-Wesley. This book was released on 2013-01-18 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field. Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance. Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure. Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s The Art of Computer Programming books—and provide the background they need to keep abreast of new research. "[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways." —From the Foreword by Donald E. Knuth

Theory of Evolutionary Computation

Author : Benjamin Doerr
Publisher : Springer Nature
ISBN 13 : 3030294145
Total Pages : 527 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Theory of Evolutionary Computation by : Benjamin Doerr

Download or read book Theory of Evolutionary Computation written by Benjamin Doerr and published by Springer Nature. This book was released on 2019-11-20 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited book reports on recent developments in the theory of evolutionary computation, or more generally the domain of randomized search heuristics. It starts with two chapters on mathematical methods that are often used in the analysis of randomized search heuristics, followed by three chapters on how to measure the complexity of a search heuristic: black-box complexity, a counterpart of classical complexity theory in black-box optimization; parameterized complexity, aimed at a more fine-grained view of the difficulty of problems; and the fixed-budget perspective, which answers the question of how good a solution will be after investing a certain computational budget. The book then describes theoretical results on three important questions in evolutionary computation: how to profit from changing the parameters during the run of an algorithm; how evolutionary algorithms cope with dynamically changing or stochastic environments; and how population diversity influences performance. Finally, the book looks at three algorithm classes that have only recently become the focus of theoretical work: estimation-of-distribution algorithms; artificial immune systems; and genetic programming. Throughout the book the contributing authors try to develop an understanding for how these methods work, and why they are so successful in many applications. The book will be useful for students and researchers in theoretical computer science and evolutionary computing.