TY - GEN
T1 - Efficient tree layout in a multilevel memory hierarchy
AU - Bender, Michael A.
AU - Demaine, Erik D.
AU - Farach-Colton, Martin
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
PY - 2002
Y1 - 2002
N2 - We consider the problem of laying out a tree or trie in a hierarchical memory, where the tree/trie has a fixed parent/child structure. The goal is to minimize the expected number of block transfers performed during a search operation, subject to a given probability distribution on the leaves. This problem was previously considered by Gil and Itai, who show optimal but high-complexity algorithms when the block-transfer size is known. We propose a simple greedy algorithm that is within an additive constant strictly less than 1 of optimal. We also present a relaxed greedy algorithm that permits more flexibility in the layout while decreasing performance (increasing the expected number of block transfers) by only a constant factor. Finally, we extend this latter algorithm to the cache-oblivious setting in which the block-transfer size is unknown to the algorithm; in particular this extension solves the problem for a multilevel memory hierarchy. The query performance of the cache-oblivious layout is within a constant factor of the query performance of the optimal layout with known block size.
AB - We consider the problem of laying out a tree or trie in a hierarchical memory, where the tree/trie has a fixed parent/child structure. The goal is to minimize the expected number of block transfers performed during a search operation, subject to a given probability distribution on the leaves. This problem was previously considered by Gil and Itai, who show optimal but high-complexity algorithms when the block-transfer size is known. We propose a simple greedy algorithm that is within an additive constant strictly less than 1 of optimal. We also present a relaxed greedy algorithm that permits more flexibility in the layout while decreasing performance (increasing the expected number of block transfers) by only a constant factor. Finally, we extend this latter algorithm to the cache-oblivious setting in which the block-transfer size is unknown to the algorithm; in particular this extension solves the problem for a multilevel memory hierarchy. The query performance of the cache-oblivious layout is within a constant factor of the query performance of the optimal layout with known block size.
UR - https://www.scopus.com/pages/publications/84938059710
U2 - 10.1007/3-540-45749-6_18
DO - 10.1007/3-540-45749-6_18
M3 - Conference contribution
AN - SCOPUS:84938059710
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 165
EP - 173
BT - Algorithms - ESA 2002 - 10th Annual European Symposium, Proceedings
A2 - Möhring, Rolf
A2 - Raman, Rajeev
PB - Springer Verlag
T2 - 10th Annual European Symposium on Algorithms, ESA 2002
Y2 - 17 September 2002 through 21 September 2002
ER -