IEEE Computer Volume 15 Number 3 -- BOOK REVIEWS
Original Publication Date: 1982-Mar-01
Included in the Prior Art Database: 2005-Nov-11
Software Patent Institute
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An Introduction to Computational Combinatorics -- E. S. Page and L. B. Wilson (Cambridge University Press, Cambridge, UK, 1979, 218 pp., $8.50).
The increasing emphasis on discrete mathematics -- especially elementary combinatorics -- in most computer science curricula has created an urgent need for introductory texts in computational discrete mathematics to supplement existing advanced texts on algorithmic graph theory, analysis of algorithms, and theory of computation. This short text by Page and Wilson fills the need for an introductory book quite well. Since it is geared to an audience with some exposure to computing and a mathematical background in elementary algebra and calculus, it is well-suited to most second-year students of computer science or computer engineering.
Chapter I discusses the problems of computational combinatorics and provides novices with a short description of how to apply combinatorial techniques to assist in both algorithm development and algorithm analysis.
The next two chapters, which introduce the mathematics of recurrence relations and difference equations, include a number of computing applications. I especially like the authors' emphasis on "looking for a reasoned argument which will relate the unknown function for a general value n . . . with values of the unknown function at one or more smaller values of n." The similarity of this approach to solving problems recursively and to modularity in structured programming is an important lesson.
The fourth chapter, "Elementary Configurations," introduces various simple combinatorial objects such as permutations, combinations, partitions, and graphs. In addition to emphasizing the employment of difference equations to enumerate these objects, the authors provide further clarification by demonstrating where these objects are encountered in practical problems.
This leads logically to Chapter 5, "Ordering arid Generation of Elementary Configurations," which adopts a computational stance. The chapter describes algorithms for generating permu...