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DOI: 10.4230/LIPIcs.ISAAC.2024.8

Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths

Authors: Sunny Atalig, Alexander Hickerson, Arrdya Srivastav, Tingting Zheng, and Marek Chrobak

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract

We consider the classical single-source shortest path problem in directed weighted graphs. D. Eppstein proved recently an Ω(n³) lower bound for oblivious algorithms that use relaxation operations to update the tentative distances from the source vertex. We generalize this result by extending this Ω(n³) lower bound to adaptive algorithms that, in addition to relaxations, can perform queries involving some simple types of linear inequalities between edge weights and tentative distances. Our model captures as a special case the operations on tentative distances used by Dijkstra’s algorithm.

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Sunny Atalig, Alexander Hickerson, Arrdya Srivastav, Tingting Zheng, and Marek Chrobak. Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{atalig_et_al:LIPIcs.ISAAC.2024.8,
  author =	{Atalig, Sunny and Hickerson, Alexander and Srivastav, Arrdya and Zheng, Tingting and Chrobak, Marek},
  title =	{{Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.8},
  URN =		{urn:nbn:de:0030-drops-221356},
  doi =		{10.4230/LIPIcs.ISAAC.2024.8},
  annote =	{Keywords: single-source shortest paths, lower bounds, decision trees}
}

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Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths

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