Cache-Oblivious Representation of B-Tree Structures
Luk\'a\v{s} Ondr\'a\v{c}ek, Ond\v{r}ej Mi\v{c}ka

TL;DR
This paper introduces CORoBTS, a cache-oblivious data structure for dynamic B-tree-like search trees that optimizes I/O operations and space efficiency, enabling efficient search, insertion, and removal in large datasets.
Contribution
The paper presents a novel cache-oblivious structure combining vEB layout with packed memory arrays, improving I/O complexity and space usage for dynamic B-trees and persistent arrays.
Findings
Achieves optimal I/O complexity of O(log_B N) for search operations.
Supports subtree insertion and removal with amortized I/O complexity involving subtree size.
Reduces space complexity of persistent array modifications from O(U^{log2 3} + V log U) to O(U + V log U).
Abstract
We propose a general data structure CORoBTS for storing B-tree-like search trees dynamically in a cache-oblivious way combining the van Emde Boas memory layout with packed memory array. In the use of the vEB layout mostly search complexity was considered, so far. We show the complexity of depth-first search of a subtree and contiguous memory area and provide better insight into the relationship between positions of vertices in tree and in memory. We describe how to build an arbitrary tree in vEB layout if we can simulate its depth-first search. Similarly, we examine batch updates of packed memory array. In CORoBTS, the stored search tree has to satisfy that all leaves are at the same depth and vertices have arity between the chosen constants and . The data structure allows searching with an optimal I/O complexity and is stored in linear space. It…
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Taxonomy
TopicsAlgorithms and Data Compression · Advanced Data Storage Technologies · Complexity and Algorithms in Graphs
