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DOI: 10.4230/LIPIcs.SEA.2026.18

DeltaSort: Incremental Sorting of Arrays with Known Updates

Authors: Shubham Dwivedi

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

When records need to be read in a particular order, sorting at query time incurs repeated Θ(n log n) cost for an array of n records and can become a bottleneck in read-heavy workloads. A common solution is to maintain a derived sorted read-replica that is kept updated as the underlying system-of-record changes. For updating read-replicas that are stored as arrays, existing approaches rely on either full re-sorting or incremental algorithms such as binary insertion or merge-based sort. In this paper, we study incremental sorting under a new model in which the sorting routine is explicitly informed of the k indices updated since the previous sort - a setting that naturally arises in systems that track updates. Under this model, we present DeltaSort, a new algorithm that runs in O(n√k) expected time using O(k) auxiliary space under a random update model, and outperforms existing algorithms for small update batches in our experimental evaluation.

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Shubham Dwivedi. DeltaSort: Incremental Sorting of Arrays with Known Updates. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dwivedi:LIPIcs.SEA.2026.18,
  author =	{Dwivedi, Shubham},
  title =	{{DeltaSort: Incremental Sorting of Arrays with Known Updates}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.18},
  URN =		{urn:nbn:de:0030-drops-260224},
  doi =		{10.4230/LIPIcs.SEA.2026.18},
  annote =	{Keywords: Incremental sorting, Sorting algorithms, Array maintenance}
}

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DeltaSort: Incremental Sorting of Arrays with Known Updates

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