Advertisement

Using Optimal Golomb Rulers for Minimizing Collisions in Closed Hashing

  • Lars Lundberg
  • Håkan Lennerstad
  • Kamilla Klonowska
  • Göran Gustafsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3321)

Abstract

We give conditions for hash table probing which minimize the expected number of collisions. A probing algorithm is determined by a sequence of numbers denoting jumps for an item during multiple collisions. In linear probing, this sequence consists of only ones – for each collision we jump to the next location. To minimize the collisions, it turns out that one should use the Golomb ruler conditions: consecutive partial sums of the jump sequence should be distinct. The commonly used quadratic probing scheme fulfils the Golomb condition for some cases. We define a new probing scheme – Golomb probing – that fulfills the Golomb conditions for a much larger set of cases. Simulations show that Golomb probing is always better than quadratic and linear and in some cases the collisions can be reduced with 25% compared to quadratic and with more than 50% compared to linear.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atkinson, L.V., Cornah, A.J.: Full period quadratic hashing. International Journal of Computer Mathematics 4(2), 177–189 (1974)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bloom, G.S., Golomb, S.W.: Applications of Numbered, Undirected Graphs. Proceedings of the IEEE 65(4), 562–571 (April 1977)CrossRefGoogle Scholar
  3. 3.
    Czech, Z.J., Havas, G., Majewski, B.S.: Perfect hashing. Theoretical Computer Science, 1–143 (1997)Google Scholar
  4. 4.
    Dimitromanolakis, A.: Analysis of the Golomb Ruler and the Sidon Set Problems, and Determination of large, near-optimal Golomb Rulers. Dept. of Electronic and Computer Engineering Technical University of Crete (June 2002)Google Scholar
  5. 5.
    Gasch, S.: Dealing with Collisions, http://www.fearme.com/misc/alg/node30.html
  6. 6.
    Hayes, B.: Computing Science: Collective Wisdom. American Scientist 98(2), 118–122 (1998)Google Scholar
  7. 7.
    Klonowska, K., Lundberg, L., Lennerstad, H.: Using Golomb Rulers for Optimal Recovery Schemes in Fault Tolerant Distributed Computing. In: Proceedings of the 17th International Parallel and Distributed Processing Symposium (IPDPS 2003), Nice, France (April 2003)Google Scholar
  8. 8.
    Lundberg, L., Haggander, D., Klonowska, K., Svahnberg, C.: Recovery schemes for high availability and high performance distributed real-time computing. In: Proceedings of the 17th International Parallel and Distributed Processing Symposium (IPDPS 2003), Nice, France (April 2003)Google Scholar
  9. 9.
    Lundberg, L., Svahnberg, C.: Optimal Recovery Schemes for High-Availability Cluster and Distributed Computing. J. Parallel Distrib. Comput. 61(11), 1680–1691 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
  11. 11.
    Standish, T.A.: Data structures in Java. Addison-Wesley, Reading (1997)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Lars Lundberg
    • 1
  • Håkan Lennerstad
    • 1
  • Kamilla Klonowska
    • 1
  • Göran Gustafsson
    • 1
  1. 1.School of EngineeringBlekinge Institute of TechnologyRonnebySweden

Personalised recommendations