The complexity of lexicographic sorting and searching

Juraj Wiedermann

Aplikace matematiky (1981)

  • Volume: 26, Issue: 6, page 432-436
  • ISSN: 0862-7940

Abstract

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An asymptotically optimal sorting algorithm that uses Θ ( n ( l o g n + k ) ) component comparisons to lexicographically sort the set of n k -tuples is presented. This sorting algorithm builds the static data structure - the so called optimal lexicographic search tree - in which it is possible to perform member searching for an unknown k -tuple in at most [ ( l o g 2 ( n + 1 ) ] + k - 1 comparisons. The number of comparisons used by this search algorithm is optimal.

How to cite

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Wiedermann, Juraj. "The complexity of lexicographic sorting and searching." Aplikace matematiky 26.6 (1981): 432-436. <http://eudml.org/doc/15214>.

@article{Wiedermann1981,
abstract = {An asymptotically optimal sorting algorithm that uses $\Theta (n(log\ n+k))$ component comparisons to lexicographically sort the set of $n$$k$-tuples is presented. This sorting algorithm builds the static data structure - the so called optimal lexicographic search tree - in which it is possible to perform member searching for an unknown $k$-tuple in at most $[(log_2(n+1)]+k-1$ comparisons. The number of comparisons used by this search algorithm is optimal.},
author = {Wiedermann, Juraj},
journal = {Aplikace matematiky},
keywords = {asymptotically optimal sorting algorithm; static data structure; lexicographic search tree; asymptotically optimal sorting algorithm; static data structure; lexicographic search tree},
language = {eng},
number = {6},
pages = {432-436},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The complexity of lexicographic sorting and searching},
url = {http://eudml.org/doc/15214},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Wiedermann, Juraj
TI - The complexity of lexicographic sorting and searching
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 6
SP - 432
EP - 436
AB - An asymptotically optimal sorting algorithm that uses $\Theta (n(log\ n+k))$ component comparisons to lexicographically sort the set of $n$$k$-tuples is presented. This sorting algorithm builds the static data structure - the so called optimal lexicographic search tree - in which it is possible to perform member searching for an unknown $k$-tuple in at most $[(log_2(n+1)]+k-1$ comparisons. The number of comparisons used by this search algorithm is optimal.
LA - eng
KW - asymptotically optimal sorting algorithm; static data structure; lexicographic search tree; asymptotically optimal sorting algorithm; static data structure; lexicographic search tree
UR - http://eudml.org/doc/15214
ER -

References

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  1. M. L. Fredman, 10.1016/0304-3975(76)90078-5, Theoretical Computer Science 1, 1976, pp. 355 - 361. (1976) Zbl0327.68056MR0416100DOI10.1016/0304-3975(76)90078-5
  2. R. L. Rivest, Partial-match retrieval algorithms, SIAM J. Computing 5, 1976, pp. 115-174. (1976) Zbl0331.68064MR0395398
  3. J. van Leeuwen, The complexity of data organisation. Foundations of computer science II, Part 1. Mathematical centre tracts 81, Mathematisch centrum, Amsterdam 1976. (1976) MR0560287
  4. J. Wiedermann, Search trees for associative retrieval, (in Slovak). Informačné systémy 1, 1979, pp. 27-41. (1979) 

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