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Linear Time LexDFS on Chordal Graphs

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

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Author Details

Jesse Beisegel
  • Brandenburg University of Technology, Cottbus, Germany
Ekkehard Köhler
  • Brandenburg University of Technology, Cottbus, Germany
Robert Scheffler
  • Brandenburg University of Technology, Cottbus, Germany
Martin Strehler
  • Brandenburg University of Technology, Cottbus, Germany

Acknowledgements

The authors would like to thank one of the anonymous referees for his or her many helpful comments.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ESA.2020.13

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).

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Trees
  • Theory of computation → Graph algorithms analysis
Keywords
  • LexDFS
  • chordal graphs
  • linear time implementation
  • search trees
  • LexBFS

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References

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