Problems on Algorithms

By William Gasarch and Ian Parberry
The ability to devise effective and efficient algorithms in new situations is a skill that separates the master programmer from the merely adequate coder. The best way to develop that skill is to solve problems. To be effective problem solvers, master-programmers-in-training must do more than memorize a collection of standard techniques and applications -- they must in addition be able to internalize and integrate what they have learned and apply it in new circumstances. This book is a collection of problems on the design, analysis, and verification of algorithms for use by practicing programmers who wish to hone and expand their skills, as a supplementary text for students enrolled in an undergraduate or beginning graduate class on algorithms, and as a self-study text for graduate students who are preparing for the qualifying (often called "breadth" or "comprehensive") examination on algorithms for a Ph.D. program in Computer Science or Computer Engineering. It is intended to augment the problem sets found in any standard algorithms textbook.
Recognizing that a supplementary text must be cost-effective if it is to be useful, the author made two important and perhaps controversial decisions in order to keep its length within reasonable bounds. The first is to cover only what it is considered to be the most important areas of algorithm design and analysis. Although most instructors throw in a "fun" advanced topic such as amortized analysis, computational geometry, approximation algorithms, number-theoretic algorithms, randomized algorithms, or parallel algorithms, it had been chosen not to cover these areas. The second decision is not to search for the origin of the problems used. A lengthy discussion of the provenance of each problem would help make this hook more scholarly, but would not make it more attractive for its intended audience -- students and practicing programmers.