Foundations and Trends® in Theoretical Computer Science > Vol 11 > Issue 3–4

Communication Complexity (for Algorithm Designers)

Tim Roughgarden, Stanford University, USA, tim@cs.stanford.edu
 
Suggested Citation
Tim Roughgarden (2016), "Communication Complexity (for Algorithm Designers)", Foundations and Trends® in Theoretical Computer Science: Vol. 11: No. 3–4, pp 217-404. http://dx.doi.org/10.1561/0400000076

Published: 11 May 2016
© 2016 T. Roughgarden
 
Subjects
Design and analysis of algorithms
 

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In this article:
Preface
1. Data Streams: Algorithms and Lower Bounds
2. Lower Bounds for One-Way Communication: Disjointness, Index, and Gap-Hamming
3. Lower Bounds for Compressive Sensing
4. Boot Camp on Communication Complexity
5. Lower Bounds for the Extension Complexity of Polytopes
6. Lower Bounds for Data Structures
7. Lower Bounds in Algorithmic Game Theory
8. Lower Bounds in Property Testing
Acknowledgements
References

Abstract

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.).

DOI:10.1561/0400000076
ISBN: 978-1-68083-114-6
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Table of contents:
Preface
1. Data Streams: Algorithms and Lower Bounds
2. Lower Bounds for One-Way Communication: Disjointness, Index, and Gap-Hamming
3. Lower Bounds for Compressive Sensing
4. Boot Camp on Communication Complexity
5. Lower Bounds for the Extension Complexity of Polytopes
6. Lower Bounds for Data Structures
7. Lower Bounds in Algorithmic Game Theory
8. Lower Bounds in Property Testing
Acknowledgements
References

Communication Complexity (for Algorithm Designers)

Communication Complexity (for Algorithm Designers) collects the lecture notes from the author’s eponymous course 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, and so on). (2) Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds.

Along the way, readers will also get exposure to a lot 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. We also scratch the surface of techniques for proving communication complexity lower bounds (fooling sets, corruption arguments, and so on).

Readers are assumed to be familiar with undergraduate-level algorithms, as well as the statements of standard large deviation inequalities (Markov, Chebyshev, and Chernoff- Hoeffding).

 
TCS-076