Distributed Computing Through Combinatorial Topology

Distributed Computing Through Combinatorial Topology, 1st Edition

Distributed Computing Through Combinatorial Topology, 1st Edition,Maurice Herlihy,Dmitry Kozlov,Sergio Rajsbaum,ISBN9780124045781

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Morgan Kaufmann




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Award-winning techniques to analyze distributed algorithms, with applications across a range of today's top computing fields

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Key Features

  • Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews
  • Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding
  • Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols
  • Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises


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.


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

Maurice Herlihy

Maurice Herlihy received an A.B. in Mathematics from Harvard University, and a Ph.D. in Computer Science from M.I.T. He has served on the faculty of Carnegie Mellon University, on the staff of DEC Cambridge Research Lab, and is currently a Professor in the Computer Science Department at Brown University. Maurice Herlihy is an ACM Fellow, and is the recipient of the 2003 Dijkstra Prize in Distributed Computing. He shared the 2004 Gödel Prize with Nir Shavit, the highest award in theoretical computer science. In 2012 he shared the Edsger W. Dijkstra Prize In Distributed Computing with Nir Shavit.

Affiliations and Expertise

Brown University, Providence, RI, USA

View additional works by Maurice Herlihy

Dmitry Kozlov

Prof. Dmitry Kozlov is recipient of the Wallenberg Prize of the Swedish Mathematics Society (2003), the Gustafsson Prize of the Goran Gustafsson Foundation (2004), and the European Prize in Combinatorics (2005). He has been a Senior Lecturer at the Royal Institute of Technology, Stockholm, and an Assistant Professor at ETH Zurich. Currently he holds the Chair of Algebra and Geometry at the University of Bremen, Germany. He is the author of the book Combinatorial Algebraic Topology published by Springer Verlag in 2008.

Affiliations and Expertise

University of Bremen, Germany

Sergio Rajsbaum

Prof. Sergio Rajsbaum is a member of the Institute of Mathematics at UNAM, where he is now a Full Professor. He has spent postdoctoral and sabbatical stays at the Massachusetts Institute of Technology and HP Research Labs. His main research interests are in the theory of distributed computing, and has about 100 publications in prestigious conferences and journals, and has been Program Committee member, and Program Chair of main forums in the area, such as the ACM Principles of Distributed Computing.

Affiliations and Expertise

Instituto de Matemáticas, Universidad Nacional Autónoma de México

Distributed Computing Through Combinatorial Topology, 1st Edition




Companion Site

Part 1: Fundamentals

Chapter 1. Introduction


1.1 Concurrency everywhere

1.2 Distributed computing

1.3 Two classic distributed computing problems

1.4 Chapter notes

1.5 Exercises

Chapter 2. Two-Process Systems


2.1 Elementary graph theory

2.2 Tasks

2.3 Models of computation

2.4 Approximate agreement

2.5 Two-process task solvability

2.6 Chapter notes

2.7 Exercises

Chapter 3. Elements of Combinatorial Topology


3.1 Basic concepts

3.2 Simplicial complexes

3.3 Standard constructions

3.4 Carrier maps

3.5 Connectivity

3.6 Subdivisions

3.7 Simplicial and continuous approximations

3.8 Chapter notes

3.9 Exercises

Part 2: Colorless Tasks

Chapter 4. Colorless Wait-Free Computation


4.1 Operational model

4.2 Combinatorial model

4.3 The computational power of wait-free colorless immediate snapshots

4.4 Chapter notes

4.5 Exercises

Chapter 5. Solvability of Colorless Tasks in Different Models


5.1 Overview of models

5.2 t-Resilient layered snapshot protocols

5.3 Layered snapshots with k-set agreement

5.4 Adversaries

5.5 Message-passing protocols

5.6 Decidability

5.7 Chapter notes

5.8 Exercises

Chapter 6. Byzantine-Resilient Colorless Computation


6.1 Byzantine failures

6.2 Byzantine communication abstractions

6.3 Byzantine set agreement

6.4 Byzantine barycentric agreement

6.5 Byzantine task solvability

6.6 Byzantine shared memory

6.7 Chapter notes

6.8 Exercises

Chapter 7. Simulations and Reductions


7.1 Motivation

7.2 Combinatorial setting

7.3 Applications

7.4 BG simulation

7.5 Conclusions

7.6 Chapter notes

7.7 Exercises

Part 3: General Tasks

Chapter 8. Read-Write Protocols for General Tasks


8.1 Overview

8.2 Tasks

8.3 Examples of tasks

8.4 Protocols

8.5 Chapter notes

8.6 Exercises

Chapter 9. Manifold Protocols


9.1 Manifold protocols

9.2 Layered immediate snapshot protocols

9.3 No set agreement from manifold protocols

9.4 Set agreement vs. weak symmetry breaking

9.5 Chapter notes

9.6 Exercises

Chapter 10. Connectivity


10.1 Consensus and path connectivity

10.2 Immediate snapshot model and connectivity

10.3 k-Set agreement and image-connectivity

10.4 Immediate snapshot model and k-connectivity

10.5 Chapter notes

10.6 Exercises

Chapter 11. Wait-Free Computability for General Tasks


11.1 Inherently colored tasks: the hourglass task

11.2 Solvability for colored tasks

11.3 Algorithm implies map

11.4 Map implies algorithm

11.5 A sufficient topological condition

11.6 Chapter notes

11.7 Exercises

Part 4: Advanced Topics

Chapter 12. Renaming and Oriented Manifolds


12.1 An upper bound: renaming with image names

12.2 Weak symmetry breaking

12.3 The index lemma

12.4 Binary colorings

12.5 A lower bound for image -renaming

12.6 Chapter notes

12.7 Exercises

Chapter 13. Task Solvability in Different Models


13.1 Shellability

13.2 Examples

13.3 Pseudospheres

13.4 Carrier maps and shellable complexes

13.5 Applications

13.6 Chapter notes

13.7 Exercises

Chapter 14. Simulations and Reductions for Colored Tasks


14.1 Model

14.2 Shared-memory models

14.3 Trivial reductions

14.4 Layered snapshot from read-write

14.5 Immediate snapshot from snapshot

14.6 Immediate snapshot from layered immediate snapshot

14.7 Snapshot from layered snapshot

14.8 Chapter Notes

14.9 Exercises

Chapter 15. Classifying Loop Agreement Tasks


15.1 The fundamental group

15.2 Algebraic signatures

15.3 Main theorem

15.4 Applications

15.5 Torsion classes

15.6 Conclusions

15.7 Chapter notes

15.8 Exercises

Chapter 16. Immediate Snapshot Subdivisions


16.1 A glimpse of discrete geometry

16.2 Chapter notes

16.3 Exercises



Quotes and reviews

"This outstanding book...explores the connections between distributed computation and topology in detail...systematically organizes material that previously was only available across a collection of conference and journal publications with inconsistent notations and terminology..."--Computing Reviews, Distributed Computing Through Combinatorial Topology

"...there has not been a monograph that comprehensively covers the intersection of topology and distributed computing...This book thus finds its place for filling precisely this niche, and will be welcomed by readers..."--Computing Reviews,July 24 2014

"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

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