License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.42
URN: urn:nbn:de:0030-drops-136875
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13687/
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Holm, Jacob ; Rotenberg, Eva

Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity

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LIPIcs-STACS-2021-42.pdf (0.8 MB)


Abstract

We present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in O(m+n) time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in worst-case O(1) time. In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case O(1) time.
As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, including planar graphs and other minor free graphs.

BibTeX - Entry

@InProceedings{holm_et_al:LIPIcs.STACS.2021.42,
  author =	{Holm, Jacob and Rotenberg, Eva},
  title =	{{Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13687},
  URN =		{urn:nbn:de:0030-drops-136875},
  doi =		{10.4230/LIPIcs.STACS.2021.42},
  annote =	{Keywords: Dynamic graphs, 2-connectivity, graph minors, r-divisions, graph separators}
}

Keywords: Dynamic graphs, 2-connectivity, graph minors, r-divisions, graph separators
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021


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