What Does Dynamic Optimality Mean in External Memory?

Michael A. Bender; Martín Farach-Colton; William Kuszmaul

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arXiv · 2201.01742

What Does Dynamic Optimality Mean in External Memory?

Michael A. Bender·Martín Farach-Colton·William Kuszmaul

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Abstract

In this paper, we revisit the question of how the dynamic optimality of search trees should be defined in external memory. A defining characteristic of external-memory data structures is that there is a stark asymmetry between queries and inserts/updates/deletes: by making the former slightly asymptotically slower, one can make the latter significantly asymptotically faster (even allowing for operations with sub-constant amortized I/Os). This asymmetry makes it so that rotation-based search trees are not optimal (or even close to optimal) in insert/update/delete-heavy external-memory workloads. To study dynamic optimality for such workloads, one must consider a different class of data structures. The natural class of data structures to consider are what we call buffered-propagation trees. Such trees can adapt dynamically to the locality properties of an input sequence in order to optimize the interactions between different inserts/updates/deletes and queries. We also present a new form of beyond-worst-case analysis that allows for us to formally study a continuum between static and dynamic optimality. Finally, we give a novel data structure, called the \jellotree, that is statically optimal and that achieves dynamic optimality for a large natural class of inputs defined by our beyond-worst-case analysis.

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Michael A. Bender, Martín Farach-Colton, William Kuszmaul. 2022-01-05. What Does Dynamic Optimality Mean in External Memory?. https://arxiv.org/abs/2201.01742

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