Belga B-Trees
Name
224_2020_9991_ReferencePDF.pdf
Size
709.51 KB
Format
Adobe PDF
Checksum (MD5)
8882e1b42ad88ca09717ae2d3c799f80
Author(s)
Demaine, Erik D.
Iacono, John
Koumoutsos, Grigorios
Langerman, Stefan
Date Issued
June 27, 2020
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
We revisitself-adjustingexternal memory tree data structures, which combine the optimal (and practical) worst-case I/O performances of B-trees, while adapting to the online distribution of queries. Our approach is analogous to undergoing efforts in the BST model, where Tango Trees (Demaine et al., SIAM J. Comput. 37(1), 240–251, 2007) were shown to be
O
(
log
log
N
)
$O(\log \log N)$
-competitive with the runtime of the best offline binary search tree on every sequence of searches. Here we formalize the B-Tree model as a natural generalization of the BST model. We prove lower bounds for the B-Tree model, and introduce a B-Tree model data structure, the Belga B-tree, that executes any sequence of searches within a
O
(
log
log
N
)
$O(\log \log N)$
factor of the best offline B-tree model algorithm, provided
B
=
log
O
(
1
)
N
$B=\log ^{O(1)}N$
. We also show how to transform any static BST into a static B-tree which is faster by a
Θ
(
log
B
)
${\varTheta }(\log B)$
factor; the transformation is randomized and we show that randomization is necessary to obtain any significant speedup.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00224-020-09991-8
