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Lower Bounds in Communication Complexity

2009 Computers
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Release : 2009
Genre : Computers
Kind : eBook
Book Rating : 585/5 ( reviews)

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Book Synopsis Lower Bounds in Communication Complexity by : Troy Lee

Download or read book Lower Bounds in Communication Complexity written by Troy Lee. This book was released on 2009. 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.

Communication Complexity

2006-11-02 Computers
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Release : 2006-11-02
Genre : Computers
Kind : eBook
Book Rating : 83X/5 ( reviews)

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Book Synopsis Communication Complexity by : Eyal Kushilevitz

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

Communication Complexity (for Algorithm Designers)

2016-05-11
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Release : 2016-05-11
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Kind : eBook
Book Rating : 146/5 ( reviews)

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Book Synopsis Communication Complexity (for Algorithm Designers) by : Tim Roughgarden

Download or read book Communication Complexity (for Algorithm Designers) written by Tim Roughgarden. This book was released on 2016-05-11. 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.

Communication Complexity

2020-02-20 Computers
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Release : 2020-02-20
Genre : Computers
Kind : eBook
Book Rating : 019/5 ( reviews)

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Book Synopsis Communication Complexity by : Anup Rao

Download or read book Communication Complexity written by Anup Rao. This book was released on 2020-02-20. 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.

Complexity Lower Bounds Using Linear Algebra

2009-07-20 Computers
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Release : 2009-07-20
Genre : Computers
Kind : eBook
Book Rating : 429/5 ( reviews)

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Book Synopsis Complexity Lower Bounds Using Linear Algebra by : Satyanarayana V. Lokam

Download or read book Complexity Lower Bounds Using Linear Algebra written by Satyanarayana V. Lokam. This book was released on 2009-07-20. 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.

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