Distributed Computing Through Combinatorial Topology


  • Maurice Herlihy, Brown University, Providence, RI, USA
  • Dmitry Kozlov, University of Bremen, Germany
  • Sergio Rajsbaum, Instituto de Matemáticas, Universidad Nacional Autónoma de México

Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols.

Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further.

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Grad / undergrad students in CS or Math; as well as working researchers or computer engineers.


Book information

  • Published: December 2013
  • ISBN: 978-0-12-404578-1


"In Distributed Computing, the modern mathematical field of Combinatorial Topology finally finds a natural application space. This book elucidates this intriguing connection through a series of well thought out examples, making complex computational phenomena and the deep theorems seem intuitive even to the beginner. I highly recommend it to anyone who is interested in the fundamentals of computing, since asynchrony, the key phenomena this book explains, is bound to dominate computation and communication in years to come."
- Prof. Nir Shavit, Professor of Computer Science, Massachusetts Institute of Technology, Cambridge, MA

“Written by the leading experts in this area, this book is a unique endeavor
covering the exciting topic of understanding distributed computing through topology.
The book will appeal to researchers in distributed computing and to mathematicians.”
- Prof. Hagit Attiya, Professor of Computer Science, Technion - Israel Institute of Technology

“This book is a major contribution to distributed computing, integrated with algebraic
topology. Based on the seminal work of the authors, it represents a collection of the most
up-to-date results in the field, presented in a very progressive manner, from intuitions
to detailed proofs and connections to fundamental mathematical concepts.”
- Éric Goubault, cea list and École Polytechnique

Table of Contents

I. Fundamentals
1. Introduction
2. Two-Process Systems
3. Elements of Combinatorial Topology

II. Colorless Tasks
4. Colorless Wait-free Computation
5. Solvability of Colorless Tasks
6. Byzantine Colorless Computation
7. Simulations and Reductions

III. General Tasks
8. Read-Write Protocols for General Tasks
9. Manifold Protocols
10. Connectivity
11. Wait-Free Computability for General Tasks

IV. Advanced Topics
12. Renaiming and Oriented Manifolds
13. Task Solvability in Different Communication Models
14. Colored Simulations and Reductions
15. Classifying Loop Agreement Tasks
16. Immediate Snapshot Subdivisions