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by Sergio Rajsbaum, Dmitry Kozlov, Maurice Herlihy
Distributed Computing Through Combinatorial Topology
Cover image
Title page
Table of Contents
Copyright
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 (k-1)-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 2n+1 names
12.2 Weak symmetry breaking
12.3 The index lemma
12.4 Binary colorings
12.5 A lower bound for 2n -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
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