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Lazy B-Trees

Authors Casper Moldrup Rysgaard , Sebastian Wild

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LIPIcs.MFCS.2025.87.pdf
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  • Theory of computation → Data structures design and analysis
Keywords
  • B-tree
  • lazy search trees
  • lazy updates
  • external memory
  • deferred data structures
  • database cracking

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Abstract

Lazy search trees (Sandlund & Wild FOCS 2020, Sandlund & Zhang SODA 2022) are sorted dictionaries whose update and query performance smoothly interpolates between that of efficient priority queues and binary search trees - automatically, depending on actual use; no adjustments are necessary to the data structure to realize the cost savings. In this paper, we design lazy B-trees, a variant of lazy search trees suitable for external memory that generalizes the speedup of B-trees over binary search trees wrt. input/output operations to the same smooth interpolation regime.
A key technical difficulty to overcome is the lack of a (fully satisfactory) external variant of biased search trees, on which lazy search trees crucially rely. We give a construction for a subset of performance guarantees sufficient to realize external-memory lazy search trees, which we deem of independent interest.
As one special case, lazy B-trees can be used as an external-memory priority queue, in which case they are competitive with some tailor-made heaps; indeed, they offer faster decrease-key and insert operations than known data structures.

Cite As Get BibTex

Casper Moldrup Rysgaard and Sebastian Wild. Lazy B-Trees. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 87:1-87:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.87

Author Details

Casper Moldrup Rysgaard
  • Aarhus University, Denmark
Sebastian Wild
  • Philipps-University Marburg, Germany
  • University of Liverpool, UK

Funding

  • Rysgaard, Casper Moldrup: Independent Research Fund Denmark, grant 9131-00113B.
  • Wild, Sebastian: EPSRC grant EP/X039447/1.

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