Computational Complexity Of Counting And Sampling

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Computational Complexity Of Counting And Sampling
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Author : Istvan Miklos
language : en
Publisher: CRC Press
Release Date : 2019-02-21
Computational Complexity Of Counting And Sampling written by Istvan Miklos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.
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
Counting Sampling And Integrating Algorithms And Complexity
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Author : Mark Jerrum
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Counting Sampling And Integrating Algorithms And Complexity written by Mark Jerrum and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.
Computational Complexity And Local Algorithms
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Author : Oded Goldreich
language : en
Publisher: Springer Nature
Release Date : 2025-07-11
Computational Complexity And Local Algorithms written by Oded Goldreich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-11 with Computers categories.
This volume contains a collection of studies in the areas of complexity theory and local algorithms. A common theme in most of the papers is the interplay between randomness and computation. This interplay is pivotal to some parts of complexity theory and is essential for local algorithms. The works included address a variety of topics in the areas of complexity theory and local algorithms. Within complexity theory the topics include approximation algorithms, counting problems, enumeration problems, explicit construction of expander graphs, fine grained complexity, interactive proof systems, PPT-search and pseudodeterminism, space complexity, and worst-case to average-case reductions. Within local algorithms the focus is mostly on property testing and on locally testable and decodable codes. In particular, many of the works seek to advance the study of testing graph properties in the bounded-degree graph model. Other topics in property testing include testing group properties and testing properties of affine subspaces.
Computational Complexity
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Author : Sanjeev Arora
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-20
Computational Complexity written by Sanjeev Arora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.
This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.
Randomization And Approximation Techniques In Computer Science
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Author : Jose D.P. Rolim
language : en
Publisher: Springer
Release Date : 2003-08-03
Randomization And Approximation Techniques In Computer Science written by Jose D.P. Rolim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-03 with Computers categories.
This book constitutes the refereed proceedings of the 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002, held in Cambridge, MA, USA in September 2002. The 21 revised full papers presented were carefully reviewed and selected from 48 submissions. Among the topics addressed are coding, geometric computations, graph colorings, random hypergraphs, graph computations, lattice computations, proof systems, probabilistic algorithms, derandomization, constraint satisfaction, and web graphs analysis.
Parameterized And Exact Computation
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Author : Hans L. Bodlaender
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-12
Parameterized And Exact Computation written by Hans L. Bodlaender and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Computers categories.
Here are the refereed proceedings of the Second International Workshop on Parameterized and Exact Computation, IWPEC 2006, held in the context of the combined conference ALGO 2006. The book presents 23 revised full papers together with 2 invited lectures. Coverage includes research in all aspects of parameterized and exact computation and complexity, including new techniques for the design and analysis of parameterized and exact algorithms, parameterized complexity theory, and more.
Techniques Of Counting
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Author : Richard Johnson
language : en
Publisher: HiTeX Press
Release Date : 2025-06-20
Techniques Of Counting written by Richard Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-20 with Computers categories.
"Techniques of Counting" "Techniques of Counting" is a comprehensive and authoritative guide that delves deeply into the art and science of enumeration, a cornerstone of combinatorics and discrete mathematics. The book commences with a meticulous treatment of fundamental counting principles—such as the sum and product rules, permutations, combinations, and critical axioms like the pigeonhole principle and inclusion-exclusion. Through crisp exposition and illustrative examples, the early chapters lay a robust groundwork, equipping readers with the essential tools needed for both elementary and intricate counting scenarios, all while seamlessly connecting to the broader framework of set theory and combinatorial identities. Building on this foundation, the text skillfully navigates advanced topics including generating functions, recurrence relations, and a rich array of combinatorial structures such as multinomials, Stirling and Bell numbers, Catalan numbers, and Ferrers diagrams. It ventures further into specialized domains, providing thorough coverage of graph enumeration, group-theoretic methods, and analytic tools like asymptotics and singularity analysis. Readers are introduced to elegant algebraic techniques, probabilistic methods, and the challenges of counting within complexity theory, with dedicated chapters on the computational hardness of counting problems, approximate algorithms, and the subtleties of constraint-based enumeration. The final chapters broaden the book’s relevance by surveying real-world applications across diverse fields. These range from error-correcting codes and cryptographic protocols to statistical mechanics, bioinformatics, and machine learning, illustrating the versatility and profound utility of combinatorial enumeration in both theory and practice. Whether for students eager to master foundational techniques or researchers seeking advanced insights, "Techniques of Counting" stands as an indispensable reference—a lucid and exhaustive resource for anyone fascinated by the universe of counting.
Walcom Algorithms And Computation
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Author : M. Sohel Rahman
language : en
Publisher: Springer
Release Date : 2018-02-21
Walcom Algorithms And Computation written by M. Sohel Rahman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-21 with Computers categories.
This book constitutes the proceedings of the 12th International Workshop on Algorithms and Computation, WALCOM 2018, held in Dhaka, Bangladesh, in March 2018. The 22 full papers presented were carefully reviewed and selected from 50 submissions. The papers cover diverse areas of algorithms and computation, such as approximation algorithms, computational geometry, combinatorial algorithms, computational biology, computational complexity, data structures, graph and network algorithms, and online algorithms.
Fundamentals Of Computation Theory
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Author : Maciej Liskiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-04
Fundamentals Of Computation Theory written by Maciej Liskiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-04 with Computers categories.
This book constitutes the refereed proceedings of the 15th International Symposium Fundamentals of Computation Theory, FCT 2005, held in Lübeck, Germany in August 2005. The 46 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on circuits, automata, complexity, approximability, computational and structural complexity, graphs and complexity, computational game theory, visual cryptography and computational geometry, query complexity, distributed systems, automata and formal languages, semantics, approximation algorithms, average case complexity, algorithms, graph algorithms, and pattern matching.
Computational Complexity
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Author : IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing
language : en
Publisher: IEEE
Release Date : 2002
Computational Complexity written by IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing and has been published by IEEE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
This text contains information on computational mathematics as presented at the 17th IEEE Annual Conference on Computational Complexity (CCC 2002).