Journal ArticleDOI
Optimal 2,3-Trees
TLDR
The 2,3-trees that are optimal in the sense of having minimal expected number of nodes visited per access are characterized in terms of their “profiles”, which leads directly to a linear-time algorithm for constructing a K-key optimal 2, 3-tree for a sorted list of K keys.Abstract:
The 2,3-trees that are optimal in the sense of having minimal expected number of nodes visited per access are characterized in terms of their “profiles”. The characterization leads directly to a linear-time algorithm for constructing a K-key optimal 2,3-tree for a sorted list of K keys. A number of results are derived that demonstrate how different in structure these optimal 2,3-trees are from their “average” cousins.read more
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Journal ArticleDOI
Ubiquitous B-Tree
TL;DR: The major variations of the B-tree are discussed, especially the B+-tree, contrasting the merits and costs of each implementation and illustrating a general purpose access method that uses a B- tree.
Journal ArticleDOI
Periodic oscillations of coefficients of power series that satisfy functional equations
TL;DR: In this article, it was shown that the coefficients an of the power series f(z) = ∑∞n=1anzn which satisfies the functional equation f (z)=z+f(z 2 +z 3 ) display periodic oscillations; a n ∼ ( o n n ) u( log n as n → ∞, where o = (1 + 5 1 2 ) 2 and u(x) is a positive, nonconstant, continuous function which is periodic with period log(4 − o).
Journal ArticleDOI
Time- and space-optimality in B-trees
TL;DR: The utility of initializing a B-tree to be compact (which initialization can be done in time linear in the number of keys if the keys are presorted) is demonstrated by comparing the space utilization of a compact tree that has been augmented by random insertions with that of a tree that have been grown entirely by random inserts.
Journal ArticleDOI
Optimum multiway search trees
TL;DR: A new general optimality principle is presented, which can be “tuned” for specific applications and considers the affects of three additional constraints, namely height, structural and node search restrictions, which lead to a number of new construction algorithms.
Journal ArticleDOI
Minimal-Comparison $2,3$-Trees
TL;DR: Those 2,3-trees that are minimal in expected number of comparisons per access for a given number of keys are characterized, and the property of comparison minimality is incompatible with the earlier-studied property of node-visit optimality.
References
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Journal ArticleDOI
Minimal-Comparison $2,3$-Trees
TL;DR: Those 2,3-trees that are minimal in expected number of comparisons per access for a given number of keys are characterized, and the property of comparison minimality is incompatible with the earlier-studied property of node-visit optimality.