Open AccessBook
Computational Complexity
Reads0
Chats0
TLDR
Computational complexity is the realm of mathematical models and techniques for establishing impossibility proofs for proving formally that there can be no algorithm for the given problem which runs faster than the current one.Abstract:
Once we have developed an algorithm (q.v.) for solving a computational problem and analyzed its worst-case time requirements as a function of the size of its input (most usefully, in terms of the O-notation; see ALGORITHMS, ANALYSIS OF), it is inevitable to ask the question: "Can we do better?" In a typical problem, we may be able to devise new algorithms for the problem that are more and more efficient. But eventually, this line of research often seems to hit an invisible barrier, a level beyond whch improvements are very difficult, seemingly impossible, to come by. After many unsuccessful attempts, algorithm designers inevitably start to wonder if there is something inherent in the problem that makes it impossible to devise algorithms that are faster than the current one. They may try to develop mathematical techniques for proving formally that there can be no algorithm for the given problem which runs faster than the current one. Such a proof would be valuable, as it would suggest that it is futile to keep working on improved algorithms for this problem, that further improvements are certainly impossible. The realm of mathematical models and techniques for establishing such impossibility proofs is called computational complexity.read more
Citations
More filters
Book
Principles of Model Checking
TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
BookDOI
Algorithms in real algebraic geometry
TL;DR: This chapter discusses computing roadmaps and Connected Components of Algebraic Sets, as well as the "complexity of Basic Algorithms" and "cylindrical Decomposition Algorithm".
Reference BookDOI
Computational Methods of Feature Selection
Huan Liu,Hiroshi Motoda +1 more
TL;DR: This book discusses Supervised, Unsupervised, and Semi-Supervised Feature Selection Key Contributions and Organization of the Book Looking Ahead Unsuper supervised Feature Selection.
Journal ArticleDOI
Extending and implementing the stable model semantics
TL;DR: A novel logic program like language, weight constraint rules, is developed for answer set programming purposes which offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.
Journal ArticleDOI
How advances in neural recording affect data analysis
TL;DR: Emerging data analysis techniques should consider both the computational costs and the potential for more accurate models associated with this exponential growth of the number of recorded neurons.
References
More filters
Journal Article
Computers and Intractability: A Guide to the Theory of NP - Completeness
Book
Algorithmics: The Spirit of Computing
David Harel,Yishai A. Feldman +1 more
TL;DR: This version of the book is published to celebrate 25 years since its first edition, and in honor of the Alan M. Turing Centennial year, and focuses on the fundamentals of computer science, which revolve around the notion of the algorithm.