Complexity Dichotomies For Counting Problems

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Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain

Author : Jin-Yi Cai
Publisher : Cambridge University Press
ISBN 13 : 1108508820
Total Pages : 473 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain by : Jin-Yi Cai

Download or read book Complexity Dichotomies for Counting Problems: Volume 1, Boolean Domain written by Jin-Yi Cai and published by Cambridge University Press. This book was released on 2017-11-16 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

Complexity Dichotomies for Counting Problems

Author : Jin-yi Cai
Publisher :
ISBN 13 : 9781107635609
Total Pages : pages
Book Rating : 4.6/5 (356 download)

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Book Synopsis Complexity Dichotomies for Counting Problems by : Jin-yi Cai

Download or read book Complexity Dichotomies for Counting Problems written by Jin-yi Cai and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics

Complexity Dichotomies for Counting Problems

Author : Jin-yi Cai
Publisher :
ISBN 13 : 9781108505840
Total Pages : pages
Book Rating : 4.5/5 (58 download)

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Book Synopsis Complexity Dichotomies for Counting Problems by : Jin-yi Cai

Complexity Dichotomies for Counting Problems

Author : Jin-Yi Cai
Publisher :
ISBN 13 : 9781108517768
Total Pages : 474 pages
Book Rating : 4.5/5 (177 download)

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Book Synopsis Complexity Dichotomies for Counting Problems by : Jin-Yi Cai

Download or read book Complexity Dichotomies for Counting Problems written by Jin-Yi Cai and published by . This book was released on 2017 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping classification theory for computational counting problems using new techniques and theories.

Complexity Dichotomies for Counting Problems

Author : Jin-Yi Cai
Publisher : Cambridge University Press
ISBN 13 : 1107062373
Total Pages : 473 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Complexity Dichotomies for Counting Problems by : Jin-Yi Cai

Download or read book Complexity Dichotomies for Counting Problems written by Jin-Yi Cai and published by Cambridge University Press. This book was released on 2017-11-16 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1. Boolean domain

Fifth International Congress of Chinese Mathematicians

Author : Lizhen Ji
Publisher : American Mathematical Soc.
ISBN 13 : 0821875876
Total Pages : 522 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fifth International Congress of Chinese Mathematicians by : Lizhen Ji

Download or read book Fifth International Congress of Chinese Mathematicians written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2012 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.

Advances in the Computational Complexity of Holant Problems

Author :
Publisher :
ISBN 13 :
Total Pages : 640 pages
Book Rating : 4.:/5 (93 download)

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Book Synopsis Advances in the Computational Complexity of Holant Problems by :

Download or read book Advances in the Computational Complexity of Holant Problems written by and published by . This book was released on 2015 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the computational complexity of counting problems defined over graphs. Complexity dichotomies are proved for various sets of problems, which classify the complexity of each problem in the set as either computable in polynomial time or \#P-hard. These problems are expressible in the frameworks of counting graph homomorphisms, counting constraint satisfaction problems, or Holant problems. However, the proofs are always expressed within the framework of Holant problems, which contains the other two frameworks as special cases. Holographic transformations are naturally expressed using this framework. They represent proofs that two different-looking problems are actually the same. We use them to prove both hardness and tractability. Moreover, the tractable cases are often stated using a holographic transformation. The uniting theme in the proofs of every dichotomy is the technical advances achieved in order to prove the hardness. Specifically, polynomial interpolation appears prominently and is indispensable. We repeatedly strengthen and extend this technique and are rewarded with dichotomies for larger and larger classes of problems. We now have a thorough understanding of its power as well as its ultimate limitations. However, fundamental questions remain since polynomial interpolation is intimately connected with integer solutions of algebraic curves and determinations of Galois groups, subjects that remain active areas of research in pure mathematics. Our motivation for this work is to understand the limits of efficient computation. Without settling the P versus #P question, the best hope is to achieve such complexity classifications.

Computing and Combinatorics

Author : Weili Wu
Publisher : Springer Nature
ISBN 13 : 3031491904
Total Pages : 424 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Computing and Combinatorics by : Weili Wu

Download or read book Computing and Combinatorics written by Weili Wu and published by Springer Nature. This book was released on 2024-01-09 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 14422-14423 constitutes the refereed proceedings of the 29th International Conference, COCOON 2023, held in Hawaii, HI, USA, during December 2023. The 60 full papers were carefully reviewed and selected from 146 submissions. They are organized in the following topical sections: Part I : Combinatorics and Algorithms; Algorithmic Solution in Applications; and Algorithm in Networks. Part II: Complexity and Approximation; Graph Algorithms; and Applied Algorithms.

Computational Complexity of Counting and Sampling

Author : Istvan Miklos
Publisher : CRC Press
ISBN 13 : 1351971611
Total Pages : 390 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Computational Complexity of Counting and Sampling by : Istvan Miklos

Download or read book Computational Complexity of Counting and Sampling written by Istvan Miklos and published by CRC Press. This book was released on 2019-02-21 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computer Science – Theory and Applications

Author : Rahul Santhanam
Publisher : Springer Nature
ISBN 13 : 3030794164
Total Pages : 485 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Computer Science – Theory and Applications by : Rahul Santhanam

Download or read book Computer Science – Theory and Applications written by Rahul Santhanam and published by Springer Nature. This book was released on 2021-06-16 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th International Computer Science Symposium in Russia, CSR 2021, held in Sochi, Russia, in June/July 2021. The 28 full papers were carefully reviewed and selected from 68 submissions. The papers cover a broad range of topics, such as formal languages and automata theory, geometry and discrete structures; theory and algorithms for application domains and much more.

Fundamentals of Computation Theory

Author : Evripidis Bampis
Publisher : Springer Nature
ISBN 13 : 3030865932
Total Pages : 476 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Fundamentals of Computation Theory by : Evripidis Bampis

Download or read book Fundamentals of Computation Theory written by Evripidis Bampis and published by Springer Nature. This book was released on 2021-09-11 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 23rd International Symposium on Fundamentals of Computation Theory, FCT 2021, held in Athens, Greece, in September 2021. The 30 full papers included in this volume were carefully reviewed and selected from 94 submissions. In addition, the book contains 2 invited talks. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.

The Complexity of Counting Problems

Author : J. D. Annan
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (535 download)

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Book Synopsis The Complexity of Counting Problems by : J. D. Annan

Download or read book The Complexity of Counting Problems written by J. D. Annan and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Complexity of Counting Problems

Author : J. D. Annan
Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (61 download)

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Book Synopsis The Complexity of Counting Problems by : J. D. Annan

Download or read book The Complexity of Counting Problems written by J. D. Annan and published by . This book was released on 1994 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intelligent Computing

Author : Kohei Arai
Publisher : Springer Nature
ISBN 13 : 3031622731
Total Pages : 588 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Intelligent Computing by : Kohei Arai

Download or read book Intelligent Computing written by Kohei Arai and published by Springer Nature. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Learning and Intelligent Optimization

Author : Dimitris E. Simos
Publisher : Springer Nature
ISBN 13 : 3030921212
Total Pages : 423 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Learning and Intelligent Optimization by : Dimitris E. Simos

Download or read book Learning and Intelligent Optimization written by Dimitris E. Simos and published by Springer Nature. This book was released on 2021-12-08 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings on Learning and Intelligent Optimization, LION 15, held in Athens, Greece, in June 2021. The 30 full papers presented have been carefully reviewed and selected from 35 submissions. LION deals with designing and engineering ways of "learning" about the performance of different techniques, and ways of using past experience about the algorithm behavior to improve performance in the future. Intelligent learning schemes for mining the knowledge obtained online or offline can improve the algorithm design process and simplify the applications of high-performance optimization methods. Combinations of different algorithms can further improve the robustness and performance of the individual components.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Graph-Theoretic Concepts in Computer Science

Author : Ignasi Sau
Publisher : Springer Nature
ISBN 13 : 3030307867
Total Pages : 394 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Graph-Theoretic Concepts in Computer Science by : Ignasi Sau

Download or read book Graph-Theoretic Concepts in Computer Science written by Ignasi Sau and published by Springer Nature. This book was released on 2019-09-11 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the revised papers of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2019, held in Vall de Núria, Spain, in June 2019. The 29 full papers presented in this volume were carefully reviewed and selected from 87 submissions. They cover a wide range of areas, aiming at connecting theory and applications by demonstrating how graph-theoretic concepts can be applied in various areas of computer science. Another focus is on presenting recent results and on identifying and exploring promising directions of future research.