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DOI: 10.4230/LIPIcs.MFCS.2021.7
Depth-First Search in Directed Planar Graphs, Revisited

Authors: Eric Allender, Archit Chauhan, and Samir Datta

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We present an algorithm for constructing a depth-first search tree in planar digraphs; the algorithm can be implemented in the complexity class AC^1(UL∩co-UL), which is contained in AC². Prior to this (for more than a quarter-century), the fastest uniform deterministic parallel algorithm for this problem was O(log^{10}n) (corresponding to the complexity class AC^{10} ⊆ NC^{11}). We also consider the problem of computing depth-first search trees in other classes of graphs, and obtain additional new upper bounds.
Cite as

Eric Allender, Archit Chauhan, and Samir Datta. Depth-First Search in Directed Planar Graphs, Revisited. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{allender_et_al:LIPIcs.MFCS.2021.7,
  author =	{Allender, Eric and Chauhan, Archit and Datta, Samir},
  title =	{{Depth-First Search in Directed Planar Graphs, Revisited}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.7},
  URN =		{urn:nbn:de:0030-drops-144478},
  doi =		{10.4230/LIPIcs.MFCS.2021.7},
  annote =	{Keywords: Depth-First Search, Planar Digraphs, Parallel Algorithms, Space-Bounded Complexity Classes}
}
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