Combinatorial algorithms : theory and practice / Edward M. Reingold, Jeorg Nievergelt, and Narsingh Deo

Includes bibliographical references and index.

What is Combinatorial Computing -- Representation of Combinatorial Objects -- Counting and Estimating -- Exhaustive Search -- Generating Elementary Combinational Objects -- Fast Search -- Sorting -- Graph Algorithms -- The Equivalence of Certain Combinatorial Problems.

he field of combinatorial algorithms concerns the problems of performing computations on discrete, finite mathematical structures. It is a new field, and only in the past few years has it started to emerge as a systematic body of knowledge instead of a collection of unrelated tricks. Its emergence as a new discipline is due to three factors: An increase in the practical importance of computation of a combinatorial nature, as compared to other computation. Rapid progress, primarily of a mathematical nature, in the design and analysis of algorithms. A shift in emphasis from the consideration of particular combinatorial algorithms to the examination of properties shared by a class of algorithms. The combination of these factors has promoted combinatorial algorithms as an important new discipline on the border between computer science and mathemaics. Courses in combinatorial algorithms and related courses in the analysis of algorithms are now being taught in colleges and universities in computer science, mathematics, electrical engineering, and operations research departments. Combinatorial algorithms can be presented in different ways, and a course or textbook can be directed toward different audiences. This book is aimed at a reader who can best be characterized as having more of a computing background than a mathematics background, a reader who is interested in combinatorial algorithms because of their practical importance.