Complexity Theory: Exploring the Limits of Efficient Algorithms

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Springer Science & Business Media, Apr 11, 2005 - Computers - 308 pages
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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.

 

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Contents

Contents
1
Algorithmic Problems Their Complexity
11
Fundamental Complexity Classes
25
4
43
The Theory of NPCompleteness 63
62
6
77
Results
99
Problems
161
Further Topics From Classical Complexity Theory
185
The Complexity of Nonuniform Problems 201
200
Communication Complexity
219
The Complexity of Boolean Functions 251
250
Final Comments
277
References
295
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About the author (2005)

The author is a full professor at the Computer Science Department of Dortmund University. He is the author of 8 monographs and more than 150 journal and conference articles. He was head of the German youth competition in computer science and has obtained the university medal for excellent teaching. He is an elected member of the German Academy of Sciences and was head of the committee reviewing computer research projects in Germany.

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