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DOI: 10.4230/LIPIcs.SWAT.2026.17
Incremental Strongly Connected Components with Predictions

Authors: Ronald Deng, Samuel McCauley, Aidin Niaparast, Helia Niaparast, Bennett Ptak, Shirel Quintanilla, Shikha Singh, and Nathan Vosburg

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the n vertices of a graph are known a priori and the m directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.
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Ronald Deng, Samuel McCauley, Aidin Niaparast, Helia Niaparast, Bennett Ptak, Shirel Quintanilla, Shikha Singh, and Nathan Vosburg. Incremental Strongly Connected Components with Predictions. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deng_et_al:LIPIcs.SWAT.2026.17,
  author =	{Deng, Ronald and McCauley, Samuel and Niaparast, Aidin and Niaparast, Helia and Ptak, Bennett and Quintanilla, Shirel and Singh, Shikha and Vosburg, Nathan},
  title =	{{Incremental Strongly Connected Components with Predictions}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.17},
  URN =		{urn:nbn:de:0030-drops-260530},
  doi =		{10.4230/LIPIcs.SWAT.2026.17},
  annote =	{Keywords: algorithms with predictions, learning augmented algorithms, incremental graph algorithms, strongly connected components, data structures}
}
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