Abstract
We present a hashing mechanism designated for real-time systems. As such, it is faster than standard hashing techniques, yet remains low-cost and uses a relatively small amount of resources. We study a mathematical model of the proposed mechanism, and compare the theoretical results to statistics obtained from simulations. The main contribution of this work is a procedure to determine the appropriate dimensions of the Hash-Table as a function of the required load, and a long-run analysis of the distribution of elements in the table.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Knuth, D.: The art of computer programming. In: Sorting and Searching, 2nd edn., vol. 3, pp. 513–558. Addison-Wesley, Reading (1998). Sect. 6.4: Hashing
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms, 21nd edn. In: Hash Tables, pp. 221–252. MIT Press, Cambridge (2001). Chap. 11
Pagiamtzis, K., Sheikholeslami, A.: Content-addressable memory (CAM) circuits and architectures: a tutorial and survey. IEEE J. Solid-State Circuits 41(3), 712–727 (2006). http://www.pagiamtzis.com/pubs/pagiamtzis-jssc2006.pdf
Wimax Forum: http://www.wimaxforum.org/
IEEE Std 802–2001. IEEE standard for local and metropolitan area networks: overview and architecture. http://standards.ieee.org/getieee802/download/802-2001.pdf
Kirsch, A., Mitzenmacher, M., Varghese, G.: Hash-based techniques for high-speed packet processing. http://www.eecs.harvard.edu/~michaelm/postscripts/dimacschapter-08.pdf
Gonnet, G.H.: Expected length of the longest probe sequence in hash code searching. J. Assoc. Comput. Mach. 28, 289–304 (1981)
Broder, A., Mitzenmacher, M.: Using multiple hash functions to improve IP lookups. In: IEEE INFOCOM 2001
Azar, Y., Broder, A., Karlin, A.R., Upfal, E.: Balanced allocations. SIAM J. Comput. 29(1), 180–200 (1999)
Vöcking, B.: How asymmetry helps load balancing. J. ACM 50(4), 568–589 (2003)
Broder, A., Karlin, A.R.: Multilevel adaptive hashing. In: Proceedings of the 1st ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 43–53 (1990)
Dietzfelbinger, M., Weidling, C.: Balanced allocation and dictionaries with tightly packed constant size bins. Theor. Comput. Sci. 380, 47–68 (2007)
Devroye, L., Morin, P.: Cuckoo hashing: further analysis. Inform. Process. Lett. 86(4), 215–219 (2003)
Pagh, R., Rodler, F.: Cuckoo hashing. J. Algorithms 51, 122–144 (2004)
Lu, Y., Montanari, A., Prabhakar, B., Dharmapurikar, S., Kabbani, A.: Counter braids: a novel counter architecture for per-flow measurement. In: Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS), 2008
Kirsch, A., Mitzenmacher, M.: The power of one move: hashing schemes for hardware. In: Proceedings of the 27th IEEE International Conference on Computer Communications (INFOCOM), 2008
Song, H., Dharmapurikar, S., Turner, J., Lockwood, J.: Fast hash table lookup using extended Bloom filter: an aid to network processing. In: Proceedings of ACM SIGCOMM, pp. 181–192 (2005)
Feistel, H.: Cryptography and computer privacy. Sci. Am. 228(5), 15–23 (1973)
Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1, 3rd edn. Wiley, New York (1968), pp. 31–32
Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 9th printing. Dover, New York (1972), p. 260
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mandelbrod, M. Layered Hashing Algorithm for Real-time Systems. Theory Comput Syst 50, 279–295 (2012). https://doi.org/10.1007/s00224-010-9297-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-010-9297-0