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DOI: 10.4230/LIPIcs.ESA.2020.13
Linear Time LexDFS on Chordal Graphs

Authors: Jesse Beisegel, Ekkehard Köhler, Robert Scheffler, and Martin Strehler

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Lexicographic Depth First Search (LexDFS) is a special variant of a Depth First Search (DFS), which was introduced by Corneil and Krueger in 2008. While this search has been used in various applications, in contrast to other graph searches, no general linear time implementation is known to date. In 2014, Köhler and Mouatadid achieved linear running time to compute some special LexDFS orderings for cocomparability graphs. In this paper, we present a linear time implementation of LexDFS for chordal graphs. Our algorithm even implements the extended version LexDFS^+ and is, therefore, able to find any LexDFS ordering for this graph class. To the best of our knowledge this is the first unrestricted linear time implementation of LexDFS on a non-trivial graph class. In the algorithm we use a search tree computed by Lexicographic Breadth First Search (LexBFS).
Cite as

Jesse Beisegel, Ekkehard Köhler, Robert Scheffler, and Martin Strehler. Linear Time LexDFS on Chordal Graphs. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{beisegel_et_al:LIPIcs.ESA.2020.13,
  author =	{Beisegel, Jesse and K\"{o}hler, Ekkehard and Scheffler, Robert and Strehler, Martin},
  title =	{{Linear Time LexDFS on Chordal Graphs}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.13},
  URN =		{urn:nbn:de:0030-drops-128790},
  doi =		{10.4230/LIPIcs.ESA.2020.13},
  annote =	{Keywords: LexDFS, chordal graphs, linear time implementation, search trees, LexBFS}
}
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