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Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms
Donald E. Knuth, Stanford University, CA
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
1997; 74 pp; softcover
Volume: 10
ISBN-10: 0-8218-0603-3
ISBN-13: 978-0-8218-0603-6
List Price: US$23
Member Price: US$18.40
Order Code: CRMP/10
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"This is a very stimulating book!"

--N. G. de Bruijn

"This short book will provide extremely enjoyable reading to anyone with an interest in discrete mathematics and algorithm design."

--Mathematical Reviews

"This book is an excellent (and enjoyable) means of sketching a large area of computer science for specialists in other fields: It requires little previous knowledge, but expects of the reader a degree of mathematical facility and a willingness to participate. It is really neither a survey nor an introduction; rather, it is a paradigm, a fairly complete treatment of a single example used as a synopsis of a larger subject."

--SIGACT News

"Anyone would enjoy reading this book. If one had to learn French first, it would be worth the effort!"

--Computing Reviews

The above citations are taken from reviews of the initial French version of this text--a series of seven expository lectures that were given at the University of Montreal in November of 1975. The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.

The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms.

Donald E. Knuth is one of the most prominent figures of modern computer science. His works in The Art of Computer Programming are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Advanced undergraduates, graduate students, and researchers interested in mathematical patterns.

Table of Contents

  • Introduction, definitions, and examples
  • Existence of a stable matching: the fundamental algorithm
  • Principle of deferred decisions: coupon collecting
  • Theoretical developments: application to the shortest path
  • Searching a table by hashing; mean behavior of the fundamental algorithm
  • Implementing the fundamental algorithm
  • Research problems
  • Annotated bibliography
  • Appendix A. Later developments
  • Appendix B. Solutions to exercises
  • Index
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