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
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. Contents:PreliminariesGreedy AlgorithmsDivide and ConquerDynamic ProgrammingOnline AlgorithmsRandomized AlgorithmsAppendix A: Number Theory and Group TheoryAppendix B: RelationsAppendix C: Logic Readership: Students of undergraduate courses in algorithms and programming. Keywords:Algorithms;Greedy;Dynamic Programming;Online;Randomized;Loop InvariantKey Features:The book is concise, and of a portable size that can be conveniently carried around by studentsIt emphasizes correctness of algorithms: how to prove them correct, which is of great importance to software engineersIt contains a chapter on randomized algorithms and applications to cryptography, as well as a chapter on online algorithms and applications to caching/paging, both of which are relevant and current topicsReviews: “Summing up, the book contains very nice introductory material for beginners in the area of correct algorithm's design.” Zentralblatt MATH
This highly structured text, in its second edition, provides comprehensive coverage of design techniques of algorithms. It traces the complete development of various algorithms in a stepwise approach followed by their pseudo-codes to build an understanding of their applications in practice. With clear explanations, the textbook intends to be much more comprehensive book on design and analysis of algorithm. Commencing with the introduction, the book gives a detailed account of graphs and data structure. It then elaborately discusses the matrix algorithms, basic algorithms, network algorithms, sorting algorithm, backtracking algorithms and search algorithms. The text also focuses on the heuristics, dynamic programming and meta heuristics. The concepts of cryptography and probabilistic algorithms have been described in detail. Finally, the book brings out the underlying concepts of benchmarking of algorithms, algorithms to schedule processor(s) and complexity of algorithms. New to the second Edition New chapters on • Matrix algorithms • Basic algorithms • Backtracking algorithms • Complexity of algorithms Several new sections including asymptotic notation, amortized analysis, recurrences, balanced trees, skip list, disjoint sets, maximal flow algorithm, parsort, radix sort, selection sort, topological sorting/ordering, median and ordered statistics, Huffman coding algorithm, transportation problem, heuristics for scheduling, etc., have been incorporated into the text.
Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a coherent and innovative manner. Written in a student-friendly style, the book emphasizes the understanding of ideas over excessively formal treatment while thoroughly covering the material required in an introductory algorithms course. Popular puzzles are used to motivate students' interest and strengthen their skills in algorithmic problem solving. Other learning-enhancement features include chapter summaries, hints to the exercises, and a detailed solution manual.
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Significant advances in DNA analysis techniques have surfaced since the 1997 publication of the bestselling An Introduction to Forensic DNA Analysis. DNA typing has become increasingly automated and miniaturized. Also, with the advent of Short Tandem Repeat (STR) technology, even the most minute sample of degraded DNA can yield a profile, providing valuable case information. However, just as the judicial system slowly and reluctantly accepted RFLP and AmpliType® PM+DQA1 typing, it is now scrutinizing the admissibility of STRs. Acknowledging STR typing as the current system of choice, An Introduction to Forensic DNA Analysis, Second Edition translates new and established concepts into plain English so that laypeople can gain insight into how DNA analysis works, from sample collection to interpretation of results. In response to the shift toward more efficient techniques, the authors cover the legal admissibility of STR typing, expand the chapter on DNA databases, and revise the section on automated analysis. They also present key decisions and appellate or supreme court rulings that provide precedent at the state and federal levels. Discussing forensic DNA issues from both a scientific and a legal perspective, the authors of An Introduction to Forensic DNA Analysis, Second Edition present the material in a manner understandable by professionals in the legal system, law enforcement, and forensic science. They cover general principles in a clear fashion and include a glossary of terms and other useful appendices for easy reference.
A course in analysis that focuses on the functions of a real variable, this text introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, theorems, and proofs. 1955 edition.
Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.