Communication Complexity (for Algorithm Designers)

ISBN-13: 9781680831146 / Angielski / Miękka / 2016 / 206 str.

Tim Roughgarden

Opis

Communication Complexity (for Algorithm Designers) collects the lecture notes from the authors 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).

Spis treści

• 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
• References