Distributed Computing Through Combinatorial Topology
1st Edition
Description
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.
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
Readership
Grad / undergrad students in CS or Math; as well as working researchers or computer engineers.
Table of Contents
Dedication
Acknowledgments
Preface
Companion Site
Part 1: Fundamentals
Chapter 1. Introduction
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
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
Abstract
10.1 Consensus and path connectivity
10.2 Immediate snapshot model and connectivity
10.3 k-Set agreement and -connectivity
10.4 Immediate snapshot model and k-connectivity
10.5 Chapter notes
10.6 Exercises
Chapter 11. Wait-Free Computability for General Tasks
Abstract
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
Abstract
12.1 An upper bound: renaming with names
12.2 Weak symmetry breaking
12.3 The index lemma
12.4 Binary colorings
12.5 A lower bound for -renaming
12.6 Chapter notes
12.7 Exercises
Chapter 13. Task Solvability in Different Models
Abstract
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
Abstract
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
Abstract
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
Abstract
16.1 A glimpse of discrete geometry
16.2 Chapter notes
16.3 Exercises
Bibliography
Index
Details
- No. of pages:
- 336
- Language:
- English
- Copyright:
- © Morgan Kaufmann 2014
- Published:
- 5th December 2013
- Imprint:
- Morgan Kaufmann
- Paperback ISBN:
- 9780124045781
- eBook ISBN:
- 9780124047280
About the Author
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
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
Awards
Notable Computing Books 2013: Computer Systems Organization, Computing Reviews
Reviews
"...very well-written. All the figures, examples, and illustrations serve nicely to explain various concepts...mathematicians and computer scientists both would equally benefit from this book...a new researcher in this area would find this book very helpful" --SIGACT News , Distributed Computing Through Combinatorial Topology
"...the first systematic exposition of an approach to distributed computing based on tools of combinatorial topology…a valuable addition to the existing literature, it will be appreciated by many different categories of readers including university students and researchers in computers science as well as topologists interested in practical applications." --Zentralblatt MATH, Distributed Computing Through Combinatorial Topology
"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