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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atkinson, L.V., Cornah, A.J.: Full period quadratic hashing. International Journal of Computer Mathematics 4(2), 177–189 (1974)
Bloom, G.S., Golomb, S.W.: Applications of Numbered, Undirected Graphs. Proceedings of the IEEE 65(4), 562–571 (April 1977)
Czech, Z.J., Havas, G., Majewski, B.S.: Perfect hashing. Theoretical Computer Science, 1–143 (1997)
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)
Gasch, S.: Dealing with Collisions, http://www.fearme.com/misc/alg/node30.html
Hayes, B.: Computing Science: Collective Wisdom. American Scientist 98(2), 118–122 (1998)
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)
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)
Lundberg, L., Svahnberg, C.: Optimal Recovery Schemes for High-Availability Cluster and Distributed Computing. J. Parallel Distrib. Comput. 61(11), 1680–1691 (2001)
Project OGR, http://www1.distributed.net/ogr/index.php.en
Standish, T.A.: Data structures in Java. Addison-Wesley, Reading (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lundberg, L., Lennerstad, H., Klonowska, K., Gustafsson, G. (2004). Using Optimal Golomb Rulers for Minimizing Collisions in Closed Hashing. In: Maher, M.J. (eds) Advances in Computer Science - ASIAN 2004. Higher-Level Decision Making. ASIAN 2004. Lecture Notes in Computer Science, vol 3321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30502-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-30502-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24087-7
Online ISBN: 978-3-540-30502-6
eBook Packages: Computer ScienceComputer Science (R0)