Información General

• Autores: Daniel H., Greene, Donald E. Knuth
• Editores: Boston (Massachusetts) : Birkhäuser, [2008
• Año de publicación: 2008
• País: Estados Unidos
• Idioma: inglés
• ISBN: 978-0-8176-4728-5
• Texto completo no disponible (Saber más ...)

Resumen

• * Collects some fundamental mathematical techniques that are required for the analysis of algorithms * Very well written: the style and the mathematical exposition make the book pleasant to read * Covers a wide range of topics in an extremely concise manner, including many of the major paradigms used in the analysis of algorithms * Contains a wealth of highly original, instructive problems and solutions taken from actual examinations given at Stanford in various computer science courses * Presents a welcome selection and careful exposition of material that can be (and is) covered in a single course with a group of advanced students well-grounded in undergraduate mathematics and computer science * Details four important topics in algorithm analysis, all from a rudimentary, but highly original, point of view: each of these topics is critical to understanding the modern analysis of algorithms, primarily from the speed of execution perspective A quantitative study of the efficiency of computer methods requires an in-depth understanding of both mathematics and computer science. This monograph, derived from an advanced computer science course at Stanford University, 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 terse enough for easy reference yet detailed enough for those with little background. Approximately half the book is devoted to original problems and solutions from examinations given at Stanford.

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Índice

• Preface
  Binomial Identities.- Summary of Useful Identities.- Deriving the Identities.- Inverse Relations.- Operator Calculus.- Hypergeometric Series.- Identities with the Harmonic Numbers
  Recurrence Relations.- Linear Recurrence Relations.- Nonlinear Recurrence Relations
  Operator Methods.- The Cookie Monster.- Coalesced Hashing.- Open Addressing: Uniform Hashing.- Open Addressing: Secondary Clustering
  Asymptotic Analysis.- Basic Concepts.- Stieltjes Integration and Asymptotics.- Asymptotics from Generating Functions
  Bibliography
  Appendices.- Schedule of Lectures.- Homework Assignments.- Midterm Exam I and Solutions.- Final Exam I and Solutions.- Midterm Exam II and Solutions.- Final Exam II and Solutions.- Midterm Exam III and Solutions.- Final Exam III and Solutions.- A Qualifying Exam Problem and Solution
  Index