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Complexity Theory : Exploring the Limits of Efficient Algorithms - Ingo Wegener

Complexity Theory

Exploring the Limits of Efficient Algorithms

By: Ingo Wegener, R. Pruim (Translator)

Hardcover

Published: 11th April 2005
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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." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

Introduction
Algorithmic Problems and Their Complexity
Fundamental Complexity Classes
Reductions - Algorithmic Relations 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
Further Complexity Classes and Relations between the Complexity Classes
Interactive Proof Systems
The PCP-Theorem and the Complexity of Approximation Problems
Classical Subjects of Complexity Theory
The Complexity of Nonuniform Problems
Communication Complexity
The Complexity of Boolean Function
Conclusions
Appendix: The O-notation
Results from Probability Theory
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540210450
ISBN-10: 3540210458
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 308
Published: 11th April 2005
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.4 x 15.6  x 1.9
Weight (kg): 1.39