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检索条件"丛书名=Foundations and trends® in theoretical computer science"

共 12 条记录，以下是1-10 订阅

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Complexity Theory, Game Theory, and Economics: The Barbados Lectures

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丛书名： foundations and trends in theoretical computer science

2020年

作者： Tim Roughgarden

ISBN: (数字)9781680836554

ISBN: (纸本)9781680836547

This monograph comprises a series of ten lectures divided into two parts. Part 1, referred to as the Solar Lectures, focuses on the communication and computational complexity of computing an (approximate) Nash equilibrium. Part 2, the Lunar Lectures, focuses on applications of computational complexity theory to game theory and economics. The goal of this short-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory, and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including several very recent breakthroughs. While the solar lectures build on each other to some extent, the lunar lectures are episodic and can be read independently of each other. Most of the lunar lectures have the flavor of “applied complexity theory” and are less technically intense. Written in a relaxed style, the author uses his didactic expertise to guide the reader through the theory in an insightful and enjoyable manner. No background in game theory is assumed, making the whole text informative and accessible to a wide audience. This monograph gives the reader an excellent introduction to the basics of the subject and highlights some of the most recent breakthroughs in research. It provides the reader with a launch pad for further research.

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Semialgebraic Proofs and Efficient Algorithm Design

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丛书名： foundations and trends® in theoretical computer science

2019年

作者： Noah Fleming Pravesh Kothari Toniann Pitassi

ISBN: (数字)9781680836370

ISBN: (纸本)9781680836363

In the last two decades a link has been established that, in some cases, proof that a solution exists has enabled an algorithm to find that solution itself. This has had most effect on semialgebraic proof systems and linear and semidefinite programming. This monograph details the interplay between proof systems and efficient algorithm design and surveys the state-of-the-art for two of the most important semi-algebraic proof systems: Sherali-Adams and Sum-of-Squares. It provides the readers with a rigorous treatment of these systems both as proof systems, and as a general family of optimization algorithms. The emphasis is on illustrating the main ideas by presenting a small fraction of representative results with detailed intuition and commentary. The monograph is self-contained and includes a review of the necessary mathematical background including basic theory of linear and semidefinite programming. Semialgebraic Proofs and Efficient Algorithm Design provides the advanced reader with a deep insight into the exciting line of research. It will inspire readers in deploying the techniques in their own further research.

关键词： computer algorithms.

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Quantum Hamiltonian Complexity

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丛书名： foundations and trends in theoretical computer science :

2015年

作者： Sevag Gharibian Yichen Huang Zeph Landau Seung Woo Shin

ISBN: (数字)9781680830071

ISBN: (纸本)9781680830064

Constraint satisfaction problems are a central pillar of modern computational complexity theory. This monograph provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity (QHC), which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a Quantum Cook-Levin Theorem to deep insights into the structure of 1D low-temperature quantum systems via so-called area laws. Quantum Hamiltonian Complexity provides the reader with a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, it includes the following: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computer-science friendly language, (3) overviews of central ideas from condensed matter physics, such as indistinguishable particles, mean field theory, tensor networks, and area laws, and (4) brief expositions of selected computer science-based results in the area. For example, as part of the latter, it provides a novel information theoretic presentation of Bravyi"s polynomial time algorithm for Quantum 2-SAT. Quantum Hamiltonian Complexity reviews some of the most fundamental results in QHC and is an ideal reference for computer scientists with little or no background in quantum information.

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Faster Algorithms Via Approximation Theory

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丛书名： foundations and trends in theoretical computer science

2014年

作者： Sushant Sachdeva Nisheeth K. Vishnoi

ISBN: (数字)9781601988218

ISBN: (纸本)9781601988201

Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.

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Algorithms and Data Structures for External Memory

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丛书名： foundations and trends in theoretical computer science Volume 2 Issue 4, 2006

2008年

作者： Jeffrey Scott Vitter

ISBN: (数字)9781601981073

ISBN: (纸本)9781601981066

Data sets in large applications are often too massive to fit completely inside the computer's internal memory. The resulting input/output communication (or I/O) between fast internal memory and slower external memory (such as disks) can be a major performance bottleneck. Algorithms and Data Structures for External Memory surveys the state of the art in the design and analysis of external memory (or EM) algorithms and data structures, where the goal is to exploit locality and parallelism in order to reduce the I/O costs. A variety of EM paradigms are considered for solving batched and online problems efficiently in external memory. Algorithms and Data Structures for External Memory describes several useful paradigms for the design and implementation of efficient EM algorithms and data structures. The problem domains considered include sorting, permuting, FFT, scientific computing, computational geometry, graphs, databases, geographic information systems, and text and string processing. Algorithms and Data Structures for External Memory is an invaluable reference for anybody interested in, or conducting research in the design, analysis, and implementation of algorithms and data structures.

关键词： computers amp the Internet computer science

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Algorithmic Results in List Decoding

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丛书名： foundations and trends R in theoretical computer science

2007年

作者： Venkatesan Guruswami

ISBN: (数字)9781601980052

ISBN: (纸本)9781601980045

Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.

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A Survey of Lower Bounds for Satisfiability and Related Problems

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丛书名： foundations and trends(R) in theoretical computer science

2007年

作者： Dieter Melkebeek

ISBN: (数字)9781601980854

ISBN: (纸本)9781601980847

NP-completeness arguably forms the most pervasive concept from computer science as it captures the computational complexity of thousands of important problems from all branches of science and engineering. The P versus NP question asks whether these problems can be solved in polynomial time. A negative answer has been widely conjectured for a long time but, until recently, no concrete lower bounds were known on general models of computation. Satisfiability is the problem of deciding whether a given Boolean formula has at least one satisfying assignment. It is the first problem that was shown to be NP-complete, and is possibly the most commonly studied NP-complete problem, both for its theoretical properties and its applications in practice. A Survey of Lower Bounds for Satisfiability and Related Problems surveys the recently discovered lower bounds for the time and space complexity of satisfiability and closely related problems. It overviews the state-of-the-art results on general deterministic, randomized, and quantum models of computation, and presents the underlying arguments in a unified framework. A Survey of Lower Bounds for Satisfiability and Related Problems is an invaluable reference for professors and students doing research in complexity theory, or planning to do so.

关键词： computers internet computer science general computers internet general

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Mathematical Aspects of Mixing Times in Markov Chains

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丛书名： foundations and trends R in theoretical computer science

2006年

作者： Ravi Montenegro Prasad Tetali

ISBN: (数字)9781933019772

ISBN: (纸本)9781933019291

Mathematical Aspects of Mixing Times in Markov Chains begins with a gentle introduction to the analytical aspects of the theory of finite Markov chain mixing times and quickly ramps up to explain the latest developments in the topic. Several theorems are revisited and often derived in simpler, transparent ways, and illustrated with examples. The highlights include spectral, logarithmic Sobolev techniques, the evolving set methodology, and issues of nonreversibility. Mathematical Aspects of Mixing Times in Markov Chains is a comprehensive, well-written review of the subject that will be of interest to researchers and students in computer and mathematical sciences.

关键词： chains foundations trends markov times aspects mixing mathematical

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Average-Case Complexity

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丛书名： foundations and trends R in theoretical computer science

2006年

作者： Andrej Bogdanov Luca Trevisan

ISBN: (数字)9781933019970

ISBN: (纸本)9781933019499

Average-Case Complexity is a thorough survey of the average-case complexity of problems in NP. The study of the average-case complexity of intractable problems began in the 1970s, motivated by two distinct applications: the developments of the foundations of cryptography and the search for methods to "cope" with the intractability of NP-hard problems. This survey looks at both, and generally examines the current state of knowledge on average-case complexity. Average-Case Complexity is intended for scholars and graduate students in the field of theoretical computer science. The reader will also discover a number of results, insights, and proof techniques whose usefulness goes beyond the study of average-case complexity.

关键词： computers amp the Internet computer science

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Pairwise Independence and Derandomization

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丛书名： "This book is originally published as foundations and trends in theoretical computer science, Volume 1 Issue 4 (2005), ISSN: 1551-305X."--Back Cover.

2006年

作者： Luby Michael George. Wigderson Avi.

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