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Dictionary look-up with small errors

  • Andrew C. Yao
  • Frances F. Yao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 937)

Abstract

Let W be a set of n binary strings of length m each. We are interested in designing data structures for W that can answer d-queries quickly, that is, given a binary string α, decide whether there is any member of W within Hamming distance d of α. This problem, originally raised by Minsky and Papert [MP], remains a challenge in data structure design. In this paper, we make an initial effort towards a theoretical study of the small d case. Our main result is a data structure that achieves O(m log log n) query time with O(nm log m) space for the d = 1 case.

Keywords

Binary String Query Time Input String Approximate String Match Exact Query 
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.

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References

  1. [DHLNP]
    D. Dolev, Y. Harari, N. Linial, N. Nisan, and M. Pamas, Neighborhood preserving hashing and approximate queries, Proceedings of Fifth ACM Symposium on Discrete Algorithms, 1994.Google Scholar
  2. [DHP]
    D. Dolev, Y. Harari and M. Parnas, Finding the neighborhood of a query in a dictionary, Proceedings of Second Israel Symposium on Theory of Computing and Systems, 1993.Google Scholar
  3. [E]
    P. Elias, Efficient storage and retrieval by content and address of static files, Journal ACM 21 (1974), 246–260.CrossRefGoogle Scholar
  4. [FKS]
    M. Fredman, M. Komlós, and E. Szemerédi, Storing a sparse table with O(1) worst case access time, Journal ACM 31 (1984), 538–544.CrossRefGoogle Scholar
  5. [GP]
    Z. Galil and K. Park, An improved algorithm for approximate string matchng, SIAM J. on Computing 19 (1990), 989–999.Google Scholar
  6. [GPY]
    D. Greene, M. Parnas and F. Yao, Multi-index hashing for information retrieval, Proceedings of 1994 IEEE Symposium on Foundations of Computer Science, November 1994, 722–731.Google Scholar
  7. [LV]
    G. Landau and U. Vishkin, Fast string matching with k differences, J. Comp. Sys. Sci. 37 (1988), 63–78.CrossRefGoogle Scholar
  8. [MW]
    U. Manber and S. Wu, An algorithm for approximate membership checking with application to password security, Information Processing Lettters 50 (1994), 191–197.Google Scholar
  9. [MP]
    M. Minsky and S. Papert, Perceptrons, MIT Press, 1969.Google Scholar
  10. [TU]
    J. Tarhio and E. Ukkonen, Approximate Boyer-Moore string matching, Report A-1990-3, Department of Computer Science, Univ. of Helsinki, March 1990.Google Scholar
  11. [U]
    E. Ukkonen, Finding approximate patterns in strings, J. Algorithms 6 (1985), 132–137.Google Scholar
  12. [UW]
    E. Ukkonen and D. Wood, Approximate string matching with suffix automata, Algorithmica 10 (1993), 353–364.CrossRefGoogle Scholar
  13. [Y]
    A. Yao, Should tables be sorted?, Journal ACM 28 (1981), 615–628.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Andrew C. Yao
    • 1
  • Frances F. Yao
    • 2
  1. 1.Department of Computer SciencePrinceton UniversityPrinceton
  2. 2.Xerox Palo Alto Research CenterPalo Alto

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