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This book is an introduction to the theory of distributed algorithms, with focus on distributed graph algorithms (network algorithms). The topics covered include:
Models of computing: precisely what is a distributed algorithm, and what do we mean when we say that a distributed algorithm solves a certain computational problem ?
Algorithm design and analysis: which computational problems can be solved with distributed algorithms, which problems can be solved efficiently, and how to do it ?
Computability and computational complexity: which computational problems cannot be solved at all with distributed algorithms, which problems cannot be solved efficiently, why is this the case, and how to prove it ?
No prior knowledge of distributed systems is needed. A basic knowledge of discrete mathematics and graph theory is assumed, as well as familiarity with the basic concepts from undergraduate-level courses on models on computation, computational complexity, and algorithms and data structures.
Foreword.
Informal Introduction
Warm-Up.
Graphs
Graph-Theoretic Foundations.
Models of Computing
PN Model: Port Numbering.
LOCAL Model: Unique Identifiers.
CONGEST Model: Bandwidth Limitations.
Randomized Algorithms.
Proving Impossibility Results
Covering Maps.
Local Neighborhoods.
Round Elimination.
Sinkless Orientation.
Hardness of Coloring.
Conclusions
Conclusions.
Hints
Bibliography