Few technical terms have gained such rapid notoriety as the appelation" NP-complete." In the short time since its introduction in the early l 970's, this term has come to symbolize the abyss of inherent intractability that algorithm designers increasingly face as they seek to solve larger and more complex problems. A wide variety of commonly encountered problems from mathematics, computer science, and operations research are now known to be NP-complete, and the collection of such problems continues to grow almost daily. Indeed, the NP-complete problems are now so pervasive that it is important for anyone concerned with the computational aspects of these fields to be familiar with the meaning and implications of this concept. This book is intended as a detailed guide to the theory of NP-completeness, emphasizing those concepts and techniques that seem to be most useful for applying the theory to practical problems. It can be viewed as consisting of three parts.

The first part, Chapters 1 through 5, covers the basic theory of NP-completeness. Chapter 1 presents a relatively low-level introduction to some of the central notions of computational complexity and discusses the significance of NP-completeness in this context. Chapters 2 through 5 provide the detailed definitions and proof techniques necessary for thoroughly understanding and applying the theory. The second part, Chapters 6 and 7, provides an overview of two alternative directions for further study. Chapter 6 concentrates on the search for efficient" approximation" algorithms for NP-complete problems, an area whose development has seen considerable interplay with the theory of NP-completeness. Chapter 7 surveys a large number of theoretical tOpics in computational complexity, many of which have arisen as a consequence of previous work on NP-completeness. Both of these chapters (especially Chapter 7) are intended solely as introductions to these areas, with our expectation being that any reader wishing to pursue particular topics in more detail will do so by consulting the cited references. The third and final part of the book is the Appendix, which contains an extensive list (more than 300 main entries, and several times this many results in total) of NP-complete and NP-hard problems. Annotations to the main entries discuss what is known about the complexity of subproblems and variants of the stated problems.