Lower Bounds In Communication Complexity

Author : Troy Lee
Publisher : Now Publishers Inc
ISBN 13 : 1601982585
Total Pages : 152 pages
Book Rating : 4.82/5 ( download)

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Download or read book Lower Bounds in Communication Complexity written by Troy Lee and published by Now Publishers Inc. This book was released on 2009 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Eyal Kushilevitz
Publisher : Cambridge University Press
ISBN 13 : 052102983X
Total Pages : 209 pages
Book Rating : 4.34/5 ( download)

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Download or read book Communication Complexity written by Eyal Kushilevitz and published by Cambridge University Press. This book was released on 2006-11-02 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.

Author : Satyanarayana V. Lokam
Publisher : Now Publishers Inc
ISBN 13 : 1601982429
Total Pages : 177 pages
Book Rating : 4.21/5 ( download)

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Download or read book Complexity Lower Bounds Using Linear Algebra written by Satyanarayana V. Lokam and published by Now Publishers Inc. This book was released on 2009-07-20 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We survey several techniques for proving lower bounds in Boolean, algebraic, and communication complexity based on certain linear algebraic approaches. The common theme among these approaches is to study robustness measures of matrix rank that capture the complexity in a given model. Suitably strong lower bounds on such robustness functions of explicit matrices lead to important consequences in the corresponding circuit or communication models. Many of the linear algebraic problems arising from these approaches are independently interesting mathematical challenges.

Author : Tim Roughgarden
Publisher : Foundations and Trends (R) in Theoretical Computer Science
ISBN 13 : 9781680831146
Total Pages : 206 pages
Book Rating : 4.43/5 ( download)

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Download or read book Communication Complexity (for Algorithm Designers) written by Tim Roughgarden and published by Foundations and Trends (R) in Theoretical Computer Science. This book was released on 2016-05-11 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Pavol Duris
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.29/5 ( download)

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Download or read book Lower Bounds on Communication Complexity written by Pavol Duris and published by . This book was released on 1983 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Anup Rao
Publisher : Cambridge University Press
ISBN 13 : 1108776019
Total Pages : 271 pages
Book Rating : 4.11/5 ( download)

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Download or read book Communication Complexity written by Anup Rao and published by Cambridge University Press. This book was released on 2020-02-20 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Springer Science & Business Media
ISBN 13 : 3662034425
Total Pages : 347 pages
Book Rating : 4.22/5 ( download)

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Download or read book Communication Complexity and Parallel Computing written by Juraj Hromkovič and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alexandre Nolin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.25/5 ( download)

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Download or read book Communication Complexity written by Alexandre Nolin and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most classical problems of communication complexity are Boolean functions. When considering functions of larger output, the way in which the result of a computation must be made available - the output model - can greatly impact the complexity of the problem. In particular, some lower bounds may not apply to all models. In this thesis, we study some lower bounds affected by the output model, problems with large outputs, revisit several classical results in the light of these output mechanisms, and relate them to the formalism of behaviors and Bell inequalities of quantum nonlocality. First, in the realm of partition bounds, we show that they necessarily have a relatively large value on large output functions, which indicates that they are lower bounds for only one of our output models. We also show how to obtain a deterministic protocol from an optimal solution of the positive partition bound, and a new connection with another lower bound technique, weak-regularity. We also leverage a recent information-theoretic re-interpretation of the partition bound to give an exponential separation between communication complexity and partition bound. The problem achieving this is a large output relation recently introduced to separate communication complexity and external information complexity. Secondly, we formally define several output models. We separate them, showing how the complexity of some problems dramatically changes between models, and for all our model re-prove standard error-reduction and randomness-removal results only previously known for the most standard, usually assumed output models. Furthermore, we show for a few natural problems that their complexity significantly varies when changing output model, and show how the rank lower bound still applies to all our models with only a slight adaptation. As last topic, we move to quantum nonlocality and show that some communication complexity lower bounds have an interpretation in the form of Bell inequalities. The Bell inequalities obtained are resistant against detection inefficiency, and a priori not against other types of disturbance. We reformulate computing a function in a specific output model as computing a behavior - a family of probability distributions indexed by possible inputs. This allows us to use the efficiency bounds as proper generalisations of the partition bound for non-standard output models.

Author : Oded Goldreich
Publisher : Springer Nature
ISBN 13 : 3030436624
Total Pages : 391 pages
Book Rating : 4.29/5 ( download)

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Download or read book Computational Complexity and Property Testing written by Oded Goldreich and published by Springer Nature. This book was released on 2020-04-03 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of studies in the areas of complexity theory and property testing. The 21 pieces of scientific work included were conducted at different times, mostly during the last decade. Although most of these works have been cited in the literature, none of them was formally published before. Within complexity theory the topics include constant-depth Boolean circuits, explicit construction of expander graphs, interactive proof systems, monotone formulae for majority, probabilistically checkable proofs (PCPs), pseudorandomness, worst-case to average-case reductions, and zero-knowledge proofs. Within property testing the topics include distribution testing, linearity testing, lower bounds on the query complexity (of property testing), testing graph properties, and tolerant testing. A common theme in this collection is the interplay between randomness and computation.

Author : University of Rochester. Dept. of Computer Science
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.18/5 ( download)

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Download or read book Lower Bounds for One-way Probabilistic Communication Complexity written by University of Rochester. Dept. of Computer Science and published by . This book was released on 1992 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We prove three different types of complexity lower bounds for the one-way unbounded-error and bounded-error error probabilistic communication protocols for boolean functions. The lower bounds are proved for arbitrary boolean functions in the common way in terms of the deterministic communication complexity of functions and in terms of the notion 'probabilistic communication characteristic' that we define. It is shown that for almost all boolean functions either the Yao's lower bound or the first or the third lower bound are more precise depending on the value of probability error.