Distributed Computing Through Combinatorial Topology

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.

• 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

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

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