Communication Complexity: and Applications

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Cambridge University Press, Feb 20, 2020 - Computers - 266 pages
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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.
 

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Contents

Introduction
1
Deterministic Protocols
9
Rank
33
Randomized Protocols
46
Numbers on Foreheads
57
Discrepancy
67
Information
93
Compressing Communication
121
Lifting
144
Circuits and Proofs
157
Memory Size
175
Data Structures
187
Extension Complexity of Polytopes
210
Distributed Computing
239
Index
250
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About the author (2020)

Anup Rao is an Associate Professor at the School of Computer Science, University of Washington. He received his Ph.D. in Computer Science from the University of Texas, Austin, and was a researcher at the Institute for Advanced Study, Princeton. His research interests are primarily in theoretical computer science.

Amir Yehudayoff is Associate Professor of Mathematics at Technion - Israel Institute of Technology, Haifa. He is interested in mathematical questions that are motivated by theoretical computer science and machine learning. He was a member of the Institute for Advanced Study in Princeton, and served as the secretary of the Israel Mathematical Union. He has won several prizes, including the Cooper Prize and the Krill Prize for excellence in scientific research, and the Kurt Mahler Prize for excellence in mathematics.

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