Computational complexity of counting and sampling
著者
書誌事項
Computational complexity of counting and sampling
（Discrete mathematics and its applications / Kenneth H. Rosen, series editor）
CRC Press, c2019
- : hardback
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注記
"A Chapman & Hall book"--Cover
Includes bibliographical references (p. 363-377) and index
内容説明・目次
内容説明
Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared toward researchers in enumerative combinatorics, discrete mathematics, and theoretical computer science.
The book covers the following topics: Counting and sampling problems that are solvable in polynomial running time, including holographic algorithms; #P-complete counting problems; and approximation algorithms for counting and sampling.
First, it opens with the basics, such as the theoretical computer science background and dynamic programming algorithms. Later, the book expands its scope to focus on advanced topics, like stochastic approximations of counting discrete mathematical objects and holographic algorithms. After finishing the book, readers will agree that the subject is well covered, as the book starts with the basics and gradually explores the more complex aspects of the topic.
Features:
Each chapter includes exercises and solutions
Ideally written for researchers and scientists
Covers all aspects of the topic, beginning with a solid introduction, before shifting to computational complexity's more advanced features, with a focus on counting and sampling
目次
1. Background on computational complexity
2. Algebraic dynamic programming and monotone computations
3. Linear algebraic algorithms. The power of subtracting
4. #P-complete counting problems
5. Holographic algorithms
6. Methods of random generations
7. Mixing of Markov chains and their applications in the theory of
counting and sampling
8. Approximable counting and sampling problems
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