Communication Complexity

and Applications

; Amir Yehudayoff

Communication Complexity

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. Les mer
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Leveringstid: Sendes innen 7 virkedager

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Communication Complexity

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.

Preface; Conventions and preliminaries; Introduction; Part I. Communication: 1. Deterministic protocols; 2. Rank; 3. Randomized protocols; 4. Numbers on foreheads; 5. Discrepancy; 6. Information; 7. Compressing communication; 8. Lifting; Part II. Applications: 9. Circuits and proofs; 10. Memory size; 11. Data structures; 12. Extension Complexity of Polytopes; 13. Distributed computing.

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

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