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.

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.

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 approximation algorithms … . It contains 16 chapters and extends from the foundations of modern complexity theory to recent developments with implications for concrete applications. … The text is well written … and the translation is successful." (Gerhard Lischke, Mathematical Reviews, Issue 2006 j) "Complexity theory is an extremely important and vivid field on the border of mathematics and computer science. … Ingo Wegener certainly created an appealing, well-written book that is a definite choice for the specialists and lecturers when an undergraduate or graduate student asks for guidance into this challenging new field of mathematics." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

Introduction into Complexity Theory with recent results With complete proofs of all results Integration of new parts of Complexity Theory as inapproximability, PCP theorem, interactive proof systems, communication complexity, black-box optimization Includes supplementary material: sn.pub/extras