Algorithms and complexity /

Wilf offers a delightful, nonstandard work (1st ed., 1986) discussing algorithms and their complexity for some problems in discrete mathematics. He essentially begins with an interesting selection of problems that range from "easy" to "hard" and from the traditional (Quicksort and some graph theory problems) to the nontraditional (matrix multiplication and the Fourier transform). In each case, a standard algorithm is discussed and analyzed, and then one or more improvements are treated. The following two chapters include 20 years of algorithmic development for the network flow problem and algorithms in number theory leading to cryptography. The author's conversational style contributes to the enjoyment of reading the thorough discussions of the algorithms and their analyses. In addition, what distinguishes this book from others in the field is the author's numerous insights on how to construct improvements and why further improvements may not be possible. At the end, "having found out something about what people know and what people don't know, the reader will have enjoyed the trip through this subject and may be interested in helping to find out a little more." ^BSumming Up: Highly recommended. Upper-division undergraduates through faculty. D. S. Larson Gonzaga University