Skip to main content
Springer Nature Link
Log in

Distributed Soft Path Coloring

  • Conference paper
  • First Online:
STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

Included in the following conference series:

  • 919 Accesses

Abstract

In a soft coloring of a graph, a few adjacent vertices may receive the same color. We study soft coloring in the distributed model where vertices are processing units and edges are communication links. We aim at reducing coloring confiicts as quickly as possible over time by recoloring. We propose a randomized algorithm for 2-coloring the path with optimal decrease rate. Confiicts can be reduced exponentially faster if extra colors are allowed. We generalize the results to a broader class of locally checkable labeling problems on enhanced paths. A single result for grid coloring is also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. B. Awerbuch, A. Goldberg, M. Luby, S. Plotkin: Network decomposition and locality in distributed computation, 30th IEEE FOCS’89

    Google Scholar 

  2. R. Cole, U. Vishkin: Deterministic coin tossing with applications to optimal parallel list ranking, Info. and Control 70 (1986), 32–53

    Article  MATH  MathSciNet  Google Scholar 

  3. G. De Marco, A. Pelc: Fast distributed graph coloring with O(δ) colors, 12th Symp. on Discrete Algorithms SODA’2001

    Google Scholar 

  4. M.S. Ermakov: Exact probabilities and asymptotics for the one-dimensional coalescing ideal gas, Stochastic Processes and their Applications 71 (1997), 275–284

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Fisch: Clustering in the one-dimensional three-color cyclic cellular automaton, Ann. Probab. 20 (1992), 1528–1548

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Fitzpatrick, L. Meertens: An experimental assessment of a stochastic, anytime, decentralized, soft colourer for sparse graphs, 1st Symp. on Stochastic Algorithms, Foundations and Applications SAGA’2001, Berlin, LNCS2264, 49–64

    Google Scholar 

  7. P. Flocchini, B. Mans, N. Santoro: Sense of direction: Definitions, properties and classes, Networks 32 (1998), 165–180

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Garg, M. Papatriantafilou, P. Tsigas: Distributed list coloring: How to dynamically allocate frequencies to mobile base stations, Wireless Networks 8 (2002), 49–60

    Article  MATH  Google Scholar 

  9. A. Goldberg, S. Plotkin, G. Shannon: Parallel symmetry-breaking in sparse graphs, 19th Symp. on Theory of Computing STOC’87, 315–324

    Google Scholar 

  10. J. Janssen, L. Naranayan: Approximation algorithms for channel asignment with constraints, 10th Int. Symp. on Algorithms and Computation ISAAC’99, 327–336

    Google Scholar 

  11. S. Kutten, D. Peleg: Fault-local distributed mending, J. Algorithms 30 (1999), 144–165

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Kutten, D. Peleg: Tight fault locality, SIAM J. Computing 30 (2000), 247–268

    Article  MATH  MathSciNet  Google Scholar 

  13. N. Linial: Locality in distributed graph algorithms, SIAM J. Computing 21 (1992), 193–201

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Mayer, M. Naor, L. Stockmeyer: Local computations in static and dynamic graphs, 3rd Israel. Symp. on Theory of Computing and Systems 1995, 268–278

    Google Scholar 

  15. R. Motwani, P. Raghavan: Randomized Algorithms, Cambridge Univ. Press 1995

    Google Scholar 

  16. M. Naor, L. Stockmeyer: What can be computed locally? SIAM J. Computing 24 (1995), 1259–1277

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Panconesi, A. Srinivasan: Randomized distributed edge coloring via an extension of the Cherno.-Hoeffding bounds, SIAM J. Computing 26 (1997), 350–368

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computing Sciences, Chalmers University, 41296, Göteborg, Sweden

    Peter Damaschke

Authors
  1. Peter Damaschke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Damaschke, P. (2003). Distributed Soft Path Coloring. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_46

Download citation

  • DOI: https://doi.org/10.1007/3-540-36494-3_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics