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Compact B-trees

Published: 30 May 1979 Publication History

Abstract

A B-tree is compact if it is minimal in number of nodes, hence has optimal space utilization, among equally capacious B-trees of the same order. The space utilization of compact B-trees is analyzed and is compared with that of noncompact B-trees and of (node)-visit-optimal B-trees, which minimize the expected number of nodes visited per key access. Compact B-trees can be as much as a factor of 2.5 more space-efficient than visit-optimal B-trees; and the node-visit cost of a compact tree is never more than 1 + the node-visit cost of an optimal tree. Finally, an in-place compactification algorithm is presented which operates in linear time in the size of the file.

References

[1]
R. Bayer and E. McCreight. Organization and maintenance of large ordered indexes. Acta Informatica 1 (3), 1972.
[2]
R. Bayer and K. Unterauer. Prefix B-trees. IBM Technical Report RJ1796, 1976.
[3]
D. E. Knuth. The Art of Computer Programming, Volume 3. Addison-Wesley, 1973.
[4]
R. E. Miller, N. Pippenger, A. L. Rosenberg, and L. Snyder. Optimal 2,3-trees. SIAM Journal of Computing 8(1), February 1979, pp. 42--59.
[5]
A. L. Rosenberg and L. Snyder. Minimal comparison 2,3-trees. SIAM Journal of Computing 7(4), November 1978, pp. 465--480.
[6]
L. Snyder. On uniquely represented data structures. Proceedings of the 18th Annual Conference on the Foundations of Computer Science, 1977.
[7]
A. C. Yao. On random 2,3-trees. Acta Informatica 9:159--170, 1978.

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cover image ACM Conferences
SIGMOD '79: Proceedings of the 1979 ACM SIGMOD international conference on Management of data
May 1979
208 pages
ISBN:089791001X
DOI:10.1145/582095
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Published: 30 May 1979

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