Experimental Variations of a Theoretically Good Retrieval Data Structure

  • Martin Aumüller
  • Martin Dietzfelbinger
  • Michael Rink
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

Abstract

A retrieval data structure implements a mapping from a set S of n keys to range R = {0,1}r, e.g. given by a list of key-value pairs (x,v) ∈ S×R, but an element outside S may be mapped to any value. Asymptotically, minimal perfect hashing allows to build such a data structure that needs nlog2e + nr + o(n) bits of memory and has constant evaluation time. Recently, data structures based on other approaches have been proposed that have linear construction time, constant evaluation time and space consumption O(nr) bits or even (1 + ε)nr bits for arbitrary ε> 0. This paper explores the practicability of one such theoretically very good proposal, bridging a gap between theory and real data structures.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Botelho, F.C., Pagh, R., Ziviani, N.: Simple and space-efficient minimal perfect hash functions. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 139–150. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Calkin, N.J.: Dependent sets of constant weight binary vectors. Combinatorics, Probability & Computing 6(3), 263–271 (1997)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Dietzfelbinger, M., Pagh, R.: Succinct data structures for retrieval and approximate membership (extended abstract). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 385–396. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Hagerup, T., Tholey, T.: Efficient minimal perfect hashing in nearly minimal space. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 317–326. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Porat, E.: An optimal Bloom filter replacement based on matrix solving. CoRR, abs/0804.1845 (2008)Google Scholar
  6. 6.
    Teitelbaum, J.: Euclid’s algorithm and the Lanczos method over finite fields. Math. Comput. 67(224), 1665–1678 (1998)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Wiedemann, D.H.: Solving sparse linear equations over finite fields. IEEE Trans. Inf. Theor. 32(1), 54–62 (1986)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Martin Aumüller
    • 1
  • Martin Dietzfelbinger
    • 1
  • Michael Rink
    • 1
  1. 1.Technische Universität IlmenauIlmenauGermany

Personalised recommendations