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An Introduction to the Analysis of Algorithms

Author: Robert Sedgewick

Publisher: Addison-Wesley

Published: 2013-01-18

Total Pages: 734

ISBN-13: 0133373487

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

Analysis of Algorithms

Author: Jeffrey J. McConnell

Publisher: Jones & Bartlett Learning

Published: 2008

Total Pages: 471

ISBN-13: 0763707821

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Data Structures & Theory of Computation

Practical Analysis of Algorithms

Author: Dana Vrajitoru

Publisher: Springer

Published: 2014-09-03

Total Pages: 475

ISBN-13: 3319098888

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This book introduces the essential concepts of algorithm analysis required by core undergraduate and graduate computer science courses, in addition to providing a review of the fundamental mathematical notions necessary to understand these concepts. Features: includes numerous fully-worked examples and step-by-step proofs, assuming no strong mathematical background; describes the foundation of the analysis of algorithms theory in terms of the big-Oh, Omega, and Theta notations; examines recurrence relations; discusses the concepts of basic operation, traditional loop counting, and best case and worst case complexities; reviews various algorithms of a probabilistic nature, and uses elements of probability theory to compute the average complexity of algorithms such as Quicksort; introduces a variety of classical finite graph algorithms, together with an analysis of their complexity; provides an appendix on probability theory, reviewing the major definitions and theorems used in the book.

Design and Analysis of Algorithms

Author: Sandeep Sen

Publisher: Cambridge University Press

Published: 2019-05-23

Total Pages: 396

ISBN-13: 1108576893

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The text covers important algorithm design techniques, such as greedy algorithms, dynamic programming, and divide-and-conquer, and gives applications to contemporary problems. Techniques including Fast Fourier transform, KMP algorithm for string matching, CYK algorithm for context free parsing and gradient descent for convex function minimization are discussed in detail. The book's emphasis is on computational models and their effect on algorithm design. It gives insights into algorithm design techniques in parallel, streaming and memory hierarchy computational models. The book also emphasizes the role of randomization in algorithm design, and gives numerous applications ranging from data-structures such as skip-lists to dimensionality reduction methods.

Beyond the Worst-Case Analysis of Algorithms

Author: Tim Roughgarden

Publisher: Cambridge University Press

Published: 2021-01-14

Total Pages: 705

ISBN-13: 1108494315

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Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.

The Design and Analysis of Algorithms

Author: Dexter C. Kozen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 327

ISBN-13: 1461244005

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These are my lecture notes from CS681: Design and Analysis of Algo rithms, a one-semester graduate course I taught at Cornell for three consec utive fall semesters from '88 to '90. The course serves a dual purpose: to cover core material in algorithms for graduate students in computer science preparing for their PhD qualifying exams, and to introduce theory students to some advanced topics in the design and analysis of algorithms. The material is thus a mixture of core and advanced topics. At first I meant these notes to supplement and not supplant a textbook, but over the three years they gradually took on a life of their own. In addition to the notes, I depended heavily on the texts • A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms. Addison-Wesley, 1975. • M. R. Garey and D. S. Johnson, Computers and Intractibility: A Guide to the Theory of NP-Completeness. w. H. Freeman, 1979. • R. E. Tarjan, Data Structures and Network Algorithms. SIAM Regional Conference Series in Applied Mathematics 44, 1983. and still recommend them as excellent references.

Mathematics for the Analysis of Algorithms

Author: Daniel H. Greene

Publisher: Springer Science & Business Media

Published: 2009-05-21

Total Pages: 141

ISBN-13: 0817647295

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This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material.

Average Case Analysis of Algorithms on Sequences

Author: Wojciech Szpankowski

Publisher: John Wiley & Sons

Published: 2011-10-14

Total Pages: 580

ISBN-13: 1118031024

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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.

An Introduction to the Analysis of Algorithms

Author: Michael Soltys

Publisher: World Scientific

Published: 2012

Total Pages: 211

ISBN-13: 9814401153

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A successor to the first edition, this updated and revised book is a great companion guide for students and engineers alike, specifically software engineers who design reliable code. While succinct, this edition is mathematically rigorous, covering the foundations of both computer scientists and mathematicians with interest in algorithms. Besides covering the traditional algorithms of Computer Science such as Greedy, Dynamic Programming and Divide & Conquer, this edition goes further by exploring two classes of algorithms that are often overlooked: Randomised and Online algorithms with emphasis placed on the algorithm itself. The coverage of both fields are timely as the ubiquity of Randomised algorithms are expressed through the emergence of cryptography while Online algorithms are essential in numerous fields as diverse as operating systems and stock market predictions. While being relatively short to ensure the essentiality of content, a strong focus has been placed on self-containment, introducing the idea of pre/post-conditions and loop invariants to readers of all backgrounds. Containing programming exercises in Python, solutions will also be placed on the book's website.

Analysis and Design of Algorithms

Author: Amrinder Arora

Publisher:

Published: 2021-03-10

Total Pages: 184

ISBN-13: 9781793520432

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Analysis and Design of Algorithms provides a structured view of algorithm design techniques in a concise, easy-to-read manner. The book was written with an express purpose of being easy - to understand, read, and carry. It presents a pioneering approach in the teaching of algorithms, based on learning algorithm design techniques, and not merely solving a collection of problems. This allows students to master one design technique at a time and apply it to a rich variety of problems. Analysis and Design of Algorithms covers the algorithmic design techniques of divide and conquer, greedy, dynamic programming, branch and bound, and graph traversal. For each of these techniques, there are templates and guidelines on when to use and not to use each technique. Many sections contain innovative mnemonics to aid the readers in remembering the templates and key takeaways. Additionally, the book covers NP-completeness and the inherent hardness of problems. The third edition includes a new section on polynomial multiplication, as well as additional exercise problems, and an updated appendix. Written with input from students and professionals, Analysis and Design of Algorithms is well suited for introductory algorithm courses at the undergraduate and graduate levels. The structured organization of the text makes it especially appropriate for online and distance learning.