License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.1
URN: urn:nbn:de:0030-drops-114973
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11497/
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Cao, Yixin ; Wang, Zhifeng ; Rong, Guozhen ; Wang, Jianxin

Graph Searches and Their End Vertices

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LIPIcs-ISAAC-2019-1.pdf (0.6 MB)

Abstract

Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al. a decade ago, and only by then we started to realize how little we understand it. Even the apparently naïve question "which vertex can be the last visited by a graph search algorithm," known as the end vertex problem, turns out to be quite elusive. We give a full picture of all maximum cardinality searches on chordal graphs, which implies a polynomial-time algorithm for the end vertex problem of maximum cardinality search. It is complemented by a proof of NP-completeness of the same problem on weakly chordal graphs. We also show linear-time algorithms for deciding end vertices of breadth-first searches on interval graphs, and end vertices of lexicographic depth-first searches on chordal graphs. Finally, we present 2^n * n^O(1)-time algorithms for deciding the end vertices of breadth-first searches, depth-first searches, and maximum cardinality searches on general graphs.

BibTeX - Entry

@InProceedings{cao_et_al:LIPIcs:2019:11497,
  author =	{Yixin Cao and Zhifeng Wang and Guozhen Rong and Jianxin Wang},
  title =	{{Graph Searches and Their End Vertices}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11497},
  URN =		{urn:nbn:de:0030-drops-114973},
  doi =		{10.4230/LIPIcs.ISAAC.2019.1},
  annote =	{Keywords: maximum cardinality search, (lexicographic) breadth-first search, (lexicographic) depth-first search, chordal graph, weighted clique graph, end verte}
}

Keywords: maximum cardinality search, (lexicographic) breadth-first search, (lexicographic) depth-first search, chordal graph, weighted clique graph, end verte
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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