Lower Bounds In Communication Complexity

Author : Troy Lee,Adi Shraibman
Publisher : Now Publishers Inc
Page : 152 pages
File Size : 47,8 Mb
Release : 2009
Category : Computers
ISBN : 9781601982582

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Lower Bounds in Communication Complexity by Troy Lee,Adi Shraibman Pdf

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 : Satyanarayana V. Lokam
Publisher : Now Publishers Inc
Page : 177 pages
File Size : 44,5 Mb
Release : 2009-07-20
Category : Computers
ISBN : 9781601982421

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Complexity Lower Bounds Using Linear Algebra by Satyanarayana V. Lokam Pdf

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 : Eyal Kushilevitz,Noam Nisan
Publisher : Cambridge University Press
Page : 209 pages
File Size : 41,6 Mb
Release : 2006-11-02
Category : Computers
ISBN : 9780521029834

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Communication Complexity by Eyal Kushilevitz,Noam Nisan Pdf

Surveys the mathematical theory and applications such as computer networks, VLSI circuits, and data structures.

Author : Tim Roughgarden
Publisher : Foundations and Trends (R) in Theoretical Computer Science
Page : 206 pages
File Size : 55,9 Mb
Release : 2016-05-11
Category : Electronic
ISBN : 1680831143

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Communication Complexity (for Algorithm Designers) by Tim Roughgarden Pdf

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 : Anup Rao,Amir Yehudayoff
Publisher : Cambridge University Press
Page : 271 pages
File Size : 42,6 Mb
Release : 2020-02-20
Category : Computers
ISBN : 9781108497985

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Communication Complexity by Anup Rao,Amir Yehudayoff Pdf

Presents basic theory for graduate students and researchers with applications in circuit and proof complexity, streaming algorithms and distributed computing.

Author : Juraj Hromkovič
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 51,8 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662034422

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Communication Complexity and Parallel Computing by Juraj Hromkovič Pdf

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 : Courant Institute of Mathematical Sciences. Computer Science Department,R. Cole,A. Siegel
Publisher : Unknown
Page : 23 pages
File Size : 47,6 Mb
Release : 1985
Category : Electronic
ISBN : OCLC:123317646

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Lower Bounds on Communication Complexity in VLSI. by Courant Institute of Mathematical Sciences. Computer Science Department,R. Cole,A. Siegel Pdf

Author : Oded Goldreich
Publisher : Springer Nature
Page : 391 pages
File Size : 55,5 Mb
Release : 2020-04-03
Category : Computers
ISBN : 9783030436629

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Computational Complexity and Property Testing by Oded Goldreich Pdf

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 : Tim Roughgarden
Publisher : Unknown
Page : 187 pages
File Size : 54,6 Mb
Release : 2016
Category : Computer algorithms
ISBN : 1680831151

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Communication Complexity (for Algorithm Designers) by Tim Roughgarden Pdf

This text collects the lecture notes from the author's course "Communication Complexity (for Algorithm Designers)," taught at Stanford in the winter quarter of 2015. The two primary goals of the text are: (1) Learn several canonical problems in communication complexity that are useful for proving lower bounds for algorithms (disjointness, index, gap-hamming, etc.). (2) Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds. Along the way, readers will also: (3) Get exposure to lots of cool computational models and some famous results about them -- data streams and linear sketches, compressive sensing, space-query time trade-offs in data structures, sublinear-time algorithms, and the extension complexity of linear programs. (4) Scratch the surface of techniques for proving communication complexity lower bounds (fooling sets, corruption arguments, etc.).

Author : Stasys Jukna
Publisher : Springer Science & Business Media
Page : 618 pages
File Size : 41,9 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9783642245084

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Boolean Function Complexity by Stasys Jukna Pdf

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.

Author : Richard Cole
Publisher : Forgotten Books
Page : 32 pages
File Size : 40,8 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 0267849249

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Lower Bounds on Communication Complexity in Vlsi (Classic Reprint) by Richard Cole Pdf

Excerpt from Lower Bounds on Communication Complexity in Vlsi We analyze a family of problems governing the vlsi complexity of broadcasting 8 bits of information in time T (s B) to each of N processors located along the perimeter of a two dimensional broadcast network. Among other results, we show. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : S. Venkatesan
Publisher : Unknown
Page : 144 pages
File Size : 53,5 Mb
Release : 1994
Category : Electronic
ISBN : CORNELL:31924073543880

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Multiprocessor Communication Complexity by S. Venkatesan Pdf

Author : Ramesh Hariharan,Madhavan Mukund,V. Vinay
Publisher : Springer
Page : 352 pages
File Size : 52,6 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540452942

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FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science by Ramesh Hariharan,Madhavan Mukund,V. Vinay Pdf

This volume contains the proceedings of the 21st international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2001), organized under the auspices of the Indian Association for Research in Computing Science (IARCS). This year’s conference attracted 73 submissions from 20 countries. Each s- mission was reviewed by at least three independent referees. In a departure from previous conferences, the ?nal selection of the papers making up the program was done through an electronic discussion spanning two weeks, without a physical meeting of the Program Committee (PC). Since the PC of FSTTCS is distributed across the globe, it is very di?cult to ?x a meeting whose time and venue is convenient for a substantial fraction of the PC. Given this, it was felt that an electronic discussion would enable all members to participate on a more equal footing in the ?nal selection. All reviews, scores, and comments were posted on a secure website, with a mechanism for making updates and automatically sending noti?cations by email to relevant members of the PC. All PC members participated actively in the discussion. The general feedback on the arrangement was very positive, so we hope to continue this in future years. We had ?ve invited speakers this year: Eric Allender, Sanjeev Arora, David Harel, Colin Stirling, and Uri Zwick. We thank them for having readily accepted our invitation to talk at the conference and for providing abstracts (and even full papers) for the proceedings.

Author : Courant Institute of Mathematical Sciences. Computer Science Department,R. Cole,A. Siegel
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 1985
Category : Electronic
ISBN : OCLC:123317646

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Lower Bounds on Communication Complexity in VLSI. by Courant Institute of Mathematical Sciences. Computer Science Department,R. Cole,A. Siegel Pdf

Author : Sanjeev Arora,Boaz Barak
Publisher : Cambridge University Press
Page : 609 pages
File Size : 43,8 Mb
Release : 2009-04-20
Category : Computers
ISBN : 9780521424264

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Computational Complexity by Sanjeev Arora,Boaz Barak Pdf

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.