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Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 3662034425
Category : Computers
Languages : en
Pages : 347
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Book Description
The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory.
Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 3662034425
Category : Computers
Languages : en
Pages : 347
Get Book Here
Book Description
The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory.
Author: Anup Rao
Publisher: Cambridge University Press
ISBN: 1108776019
Category : Computers
Languages : en
Pages : 271
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Book Description
Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.
Author: Juraj Hromkovič
Publisher:
ISBN:
Category :
Languages : en
Pages : 336
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Book Description
Author: Tomasz Jurdziński
Publisher: Springer Nature
ISBN: 3030795276
Category : Computers
Languages : en
Pages : 389
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Book Description
This book constitutes the refereed conference proceedings of the 28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021, held in Wrocław, Poland, in June 2021. Due to COVID-19, the conference will be held online. The 20 full papers presented in this book were carefully reviewed and selected from 48 submissions. The papers are solicited from all areas of study of local structural knowledge and global communication and computational complexities. Among the typical areas are distributed computing, communication networks, game theory, parallel computing, social networks, mobile computing
Author: Juraj Hromkovič (Informatiker)
Publisher:
ISBN: 9787506247368
Category : Computational complexity
Languages : en
Pages : 336
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Book Description
Author: Tim Roughgarden
Publisher: Foundations and Trends (R) in Theoretical Computer Science
ISBN: 9781680831146
Category :
Languages : en
Pages : 206
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Book Description
This book deals mostly with impossibility results - lower bounds on what can be accomplished by algorithms. However, the perspective is unapologetically that of an algorithm designer. The reader will learn lower bound technology on a "need-to-know" basis, guided by fundamental algorithmic problems that we care about.
Author: Dimitri Bertsekas
Publisher: Athena Scientific
ISBN: 1886529159
Category : Mathematics
Languages : en
Pages : 832
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Book Description
This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.
Author: Raymond Greenlaw
Publisher: Oxford University Press, USA
ISBN: 0195085914
Category : Computational complexity
Languages : en
Pages : 328
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Book Description
This book provides a comprehensive analysis of the most important topics in parallel computation. It is written so that it may be used as a self-study guide to the field, and researchers in parallel computing will find it a useful reference for many years to come. The first half of the book consists of an introduction to many fundamental issues in parallel computing. The second half provides lists of P-complete- and open problems. These lists will have lasting value to researchers in both industry and academia. The lists of problems, with their corresponding remarks, the thorough index, and the hundreds of references add to the exceptional value of this resource. While the exciting field of parallel computation continues to expand rapidly, this book serves as a guide to research done through 1994 and also describes the fundamental concepts that new workers will need to know in coming years. It is intended for anyone interested in parallel computing, including senior level undergraduate students, graduate students, faculty, and people in industry. As an essential reference, the book will be needed in all academic libraries.
Author: Eyal Kushilevitz
Publisher: Cambridge University Press
ISBN: 052102983X
Category : Computers
Languages : en
Pages : 209
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Book Description
Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.
Author: Troy Lee
Publisher: Now Publishers Inc
ISBN: 1601982585
Category : Computers
Languages : en
Pages : 152
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Book Description
The communication complexity of a function f(x, y) measures the number of bits that two players, one who knows x and the other who knows y, must exchange to determine the value f(x, y). Communication complexity is a fundamental measure of complexity of functions. Lower bounds on this measure lead to lower bounds on many other measures of computational complexity. This monograph surveys lower bounds in the field of communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to find a geometric complexity measure, such as rank or trace norm, that serves as a lower bound to the underlying communication complexity measure. Lower bounds on this geometric complexity measure are then found using algebraic and geometric tools.
