Advertisement

Simplified Witness Tree Arguments

  • Thomas Schickinger
  • Angelika Steger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1963)

Abstract

In this paper we survey some results concerning balls-intobins- games and the power of two choices. We present a unified and rather elementary analysis for models in the parallel as well as in the sequential setting which is based on witness trees.

Keywords

Communication Round Cross Edge Sequential Arrival Witness Tree Multistage Interconnection Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Micah Adler, Soumen Chakrabarti, Michael Mitzenmacher, and Lars Rasmussen. Parallel randomized load balancing. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (STOC-95), pages 238–247. ACM Press, 1995. 72, 73Google Scholar
  2. 2.
    Yossi Azar, Andrej Broder, Anna R. Karlin, and Eli Upfal. Balanced allocations. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing (STOC-94), pages 593–602, 1994. 71, 73, 79, 82Google Scholar
  3. 3.
    Petra Berenbrink, Artur Czumaj, Angelika Steger, and Berthold Vöcking. Balanced allocation: the heavily loaded case. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC-00), pages 745–754, 2000. 73Google Scholar
  4. 4.
    Richard Cole, Alan Frieze, Bruce M. Maggs, Michael Mitzenmacher, Andréa W. Richa, Ramesh K. Sitaraman, and Eli Upfal. On balls and bins with deletions. In Proceedings of the 2nd International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM), 1998.Google Scholar
  5. 5.
    Richard Cole, Bruce M. Maggs, Friedhelm Meyer auf der Heide, Michael Mitzenmacher, Andrea W. Richa, Klaus Schröder, Ramesh K. Sitaraman, and Berthold Vöcking. Randomized protocols for low-congestion circuit routing in multistage interconnection networks. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 378–388, 1998.Google Scholar
  6. 6.
    Artur Czumaj, Friedhelm Meyer auf der Heide, and Volker Stemann. Improved optimal shared memory simulations, and the power of reconfiguration. In Proceedings of the 3rd Israel Symposium on Theory of Computing, pages 11–19, 1995.Google Scholar
  7. 7.
    Artur Czumaj and Volker Stemann. Randomized allocation processes. In Proceedings of the 38th IEEE Symposium on the Foundations of Computer Science (FOCS-97), pages 194–203, 1997. 73Google Scholar
  8. 8.
    Martin Dietzfelbinger and Friedhelm Meyer auf der Heide. Simple, efficient shared memory simulations (extended abstract). In Proceedings of the 5th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA-93), pages 110–119, 1993.Google Scholar
  9. 9.
    Leslie Ann Goldberg, Yossi Matias, and Satish Rao. An optical simulation of shared memory. In Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA-94), pages 257–267, New York, 1994. ACM Press.Google Scholar
  10. 10.
    Gaston H. Gonnet. Expected length of the longest probe sequence in hash code searching. Journal of the ACM, 28(2):289–304, 1981. 71zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Richard M. Karp, Michael Luby, and Friedhelm Meyer auf der Heide. Efficient PRAM simulation on a distributed memory machine. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing (STOC-92), pages 318–326. ACM Press, 1992.Google Scholar
  12. 12.
    Philip. D. MacKenzie, C. Greg Plaxton, and Rajmohan Rajaraman. On contention resolution protocols and associated probabilistic phenomena. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing (STOC-94), pages 153–162, 1994.Google Scholar
  13. 13.
    Friedhelm Meyer auf der Heide, Christian Scheideler, and Volker Stemann. Exploiting storage redundancy to speed up randomized shared memory simulations. In Proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS-95), volume LNCS 900, pages 267–278. Springer-Verlag, 1995.Google Scholar
  14. 14.
    Michael Mitzenmacher. Density dependent jump markov processes and applications to load balancing. In Proceedings of the 37th IEEE Symposium on Foundations (FOCS-96), pages 213–223, 1996.Google Scholar
  15. 15.
    Michael Mitzenmacher. On the Power of Two Choices in Randomized Load Balancing. PhD thesis, 1996. 71Google Scholar
  16. 16.
    Michael Mitzenmacher. On the analysis of randomized load balancing schemes. In Proceedings of the 9th Annual ACM Symposium on Parallel Algorithms and Arrays (SPAA-97), pages 292–301, 1997.Google Scholar
  17. 17.
    Martin Raaban and Angelika Steger. Balls into bins—a simple and tight analysis. In Proceedings of the 2nd International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM-98), volume LNCS 1518, pages 159–170, 1998Google Scholar
  18. 18.
    Volker Stemann. Parallel balanced allocations. In Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA-96), pages 261–269, 1996.Google Scholar
  19. 19.
    Berthold Vöcking. How asymmetry helps load balancing. In Proceedings of the 40th IEEE Symposium on Foundations of Computer Science (FOCS-99), pages 131–140, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas Schickinger
    • 1
  • Angelika Steger
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany

Personalised recommendations