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Optimal trees for searching in codebook

  • Ivan Kopeček
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1338)

Abstract

Finding nearest neighbour of a given vector in a codebook leads to the following model of searching. In a metric space V, a vector x and a finite subset of vectors S (representing a codebook) are given. We have to find an element of S which is „nearest” to the element x. In what follows, the problem is formulated more exactly and a characterization of optimal search trees for this model of searching is given. It turns out, that balanced quasi-ternary trees are optimal search trees for the discussed problem. The result enables to speed up fording a codebook representation vector of a given acoustic vector, which is important for applications in speech recognition and synthesis.

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References

  1. 1.
    M. Berka, I. Kopeček. Optimality of Decision Structures of Information Systems. 16th IFIP Conference on System Modelling and Optimization, 1993, pages 653–657.Google Scholar
  2. 2.
    D.Y. Cheng, A. Gerscho. A Fast Codebook Search Algorithm for Nearest-Neighbour Pattern Matching. Proc ICASSP 86, Tokyo 1986, pages 265–268.Google Scholar
  3. 3.
    R.M. Gray. Vector Quantization. IEEE ASSP Magazine, 1, 1984, pages 4–29.Google Scholar
  4. 4.
    I. Kopeček. Speech Synthesis of Czech Language in Time Domain and Applications for Visually Impaired. Proceedings of the 2-nd SQEL Workshop, Plzeň 1997, pages 141–144.Google Scholar
  5. 5.
    D. E. Knuth. The Art of Computer Programming. Volume 3-Sorting and Searching. Addison-Wesley, 1973.Google Scholar
  6. 6.
    W. Mayeda. Graph Theory. New York, Wiley 1972.Google Scholar
  7. 7.
    J. Wiedermann. Searching. SNTL, Praha 1991 (in Czech).Google Scholar
  8. 8.
    T.P. Yunck. A Technique to Identify Nearest Neighbours. IEEE Trans. Syst. 6(76), pages 678–683.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ivan Kopeček
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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