P, NP, and NP-Completeness
The Basics of Computational Complexity

Starting from the basics of computability, this undergraduate introduction focuses on the P versus NP Question and the theory of NP-completeness.

Oded Goldreich (Author)

9780521192484, Cambridge University Press

Hardback, published 16 August 2010

216 pages, 18 b/w illus. 94 exercises
22.9 x 14.7 x 1.8 cm, 0.49 kg

'The author is a well-known expert in the field of complexity theory and so is well-qualified to bring out this book which will serve as a very good introductory textbook. The focus on search problems and promise problems in this book is to be appreciated since many books neglect these topics.' S. V. Naaraj, SIGACT News

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

1. Computational tasks and models
2. The P versus NP Question
3. Polynomial-time reductions
4. NP-completeness
5. Three relatively advanced topics
Epilogue: a brief overview of complexity theory.

Subject Areas: Mathematical theory of computation [UYA], Algorithms & data structures [UMB]