Complexity Theory Exploring the Limits of Efficient Algorithms [Paperback]

Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models

All topics are considered from an algorithmic point of view stressing the implications for algorithm design

Complexity theory is the theory of determining the necessary resources for the solution of algorithmic problems and, therefore, the limits of what is possible with the available resources. An understanding of these limits prevents the search for non-existing efficient algorithms. This textbook considers randomization as a key concept and emphasizes the interplay between theory and practice:

New branches of complexity theory continue to arise in response to new algorithmic concepts, and its results - such as the theory of NP-completeness - have influenced the development of all areas of computer science.

The topics selected have implications for concrete applications, and the significance of complexity theory for today's computer science is stressed throughout.

Algorithmic Problems & Their Complexity.- Fundamental Complexity Classes.- Reductions  Algorithmic Relationships Between Problems.- The Theory of NP-Completeness.- NP-complete and NP-equivalent Problems.- The Complexity Analysis of Problems.- The Complexity of Approximation Problems  Classical Results.- The Complexity of Black Box Problems.- Additional Complexity Classes and Relationships Between Complexity Classes.- Interactive Proofs.- The PCP Theorem and the Complexity of Approximation Problems.- Further Topics From Classical Complexity Theory.- The Complexity of Non-uniform Problems.- Communication Complexity.- The Complexity of Boolean Functions.

From the reviews:

This book should be important and useful for students of computer science as an introduction to complexity theory with an emphasis on randomized and alc7