Distributed graph coloring fundamentals and recent developments /

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The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n -vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discre...

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Bibliographic Details
Main Author: Barenboim, Leonid
Other Authors: Elkin, Michael
Format: eBook
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, c2013.
Series:Synthesis digital library of engineering and computer science.
Synthesis lectures on distributed computing theory ; # 11.
Subjects:
Broken symmetry (Physics)
Electronic data processing > Distributed processing.
Graph coloring > Mathematical models.
arboricity
coloring
deterministic algorithms
distributed symmetry breaking
maximal independent set
maximal matching
randomized algorithms
Online Access:Abstract with links to full text
Table of Contents:
  • 1. Introduction
  • 10. Introduction to distributed randomized algorithms
  • 10.1 Simple algorithms
  • 10.2 A faster O([delta])-coloring algorithm
  • 10.3 Randomized MIS
  • 10.3.1 A high-level description
  • 10.3.2 Procedure decide
  • 10.4 Randomized maximal matching
  • 10.5 Graphs with bounded arboricity
  • 11. Conclusion and open questions
  • 11.1 Problems that can be solved in polylogarithmic time
  • 11.2 Problems that can be solved in (sub)linear in [delta] time
  • 11.3 Algorithms for restricted graph families
  • 11.4 Randomized algorithms
  • 2. Basics of graph theory
  • 2.1 Graphs with large girth and large chromatic number
  • 2.2 Planar graphs
  • 2.3 Arboricity
  • 2.3.1 Nash-Williams theorem
  • 2.3.2 Degeneracy and arboricity
  • 2.4 Defective coloring
  • 2.5 Edge-coloring and matchings
  • 3. Basic distributed graph coloring algorithms
  • 3.1 The distributed message-passing LOCAL model
  • 3.2 Basic color reduction
  • 3.3 Orientations
  • 3.4 The algorithm of Cole and Vishkin
  • 3.5 Extensions to graphs with bounded maximum degree
  • 3.6 An improved coloring algorithm for graphs with bounded maximum degree
  • 3.7 A faster ([delta plus] 1)-coloring
  • 3.8 Kuhn-Wattenhofer color reduction technique and its applications
  • 3.9 A reduction from ([delta plus] 1)-coloring to MIS
  • 3.10 Linial's algorithm
  • 4. Lower bounds
  • 4.1 Coloring unoriented trees
  • 4.1.1 The first proof
  • 4.1.2 The second proof
  • 4.2 Coloring the n-path Pn
  • 5. Forest-decomposition algorithms and applications
  • 5.1 H-partition
  • 5.2 An O(a)-coloring
  • 5.3 Faster coloring
  • 5.4 MIS algorithms
  • 6. Defective coloring
  • 6.1 Employing defective coloring for computing legal coloring
  • 6.2 Defective coloring algorithms
  • 6.2.1 Procedure refine
  • 6.2.2 Procedure defective-color
  • 7. Arbdefective coloring
  • 7.1 Small arboricity decomposition
  • 7.2 Efficient coloring algorithms
  • 8. Edge-coloring and maximal matching
  • 8.1 Edge-coloring and maximal matching using forest-decomposition
  • 8.2 Edge-coloring using bounded neighborhood independence
  • 9. Network decompositions
  • 9.1 Applications of network decompositions
  • 9.2 Ruling sets and forests
  • 9.3 Constructing network decompositions
  • Bibliography
  • Authors' biographies.

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