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Decremental SPQR-trees for Planar Graphs

Authors Jacob Holm , Giuseppe F. Italiano , Adam Karczmarz , Jakub Lacki , Eva Rotenberg

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Author Details

Jacob Holm
  • University of Copenhagen, Denmark
Giuseppe F. Italiano
  • University of Rome Tor Vergata, Italy
Adam Karczmarz
  • University of Warsaw, Poland
Jakub Lacki
  • Google Research, USA
Eva Rotenberg
  • Technical University of Denmark, Denmark

Funding

  • Holm, Jacob: Jacob Holm is supported by Mikkel Thorup’s Advanced Grant DFF-0602-02499B from the Danish Council for Independent Research under the Sapere Aude research career programme.
  • Italiano, Giuseppe F.: Giuseppe F. Italiano is partially supported by the Italian Ministry of Education, University and Research under Project AMANDA (Algorithmics for MAssive and Networked DAta).
  • Karczmarz, Adam: Adam Karczmarz is supported by the grants 2014/13/B/ST6/01811 and 2017/24/T/ST6/00036 of the Polish National Science Center.
  • Lacki, Jakub: When working on this paper Jakub Łącki was partly supported by the EU FET project MULTIPLEX no. 317532 and the Google Focused Award on "Algorithms for Large-scale Data Analysis" and Polish National Science Center grant number 2014/13/B/ST6/01811. Part of this work was done while Jakub Łącki was visiting the Simons Institute for the Theory of Computing.

Cite As Get BibTex

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, and Eva Rotenberg. Decremental SPQR-trees for Planar Graphs. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ESA.2018.46

Abstract

We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over Omega(n) operations, is O(log^2 n). Via SPQR-trees, we give a decremental data structure for maintaining 3-vertex connectivity in planar graphs. It answers queries in O(1) time and processes edge deletions and contractions in O(log^2 n) amortized time. The previous best supported deletions and insertions in O(sqrt{n}) time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Data structures design and analysis
Keywords
  • Graph embeddings
  • data structures
  • graph algorithms
  • planar graphs
  • SPQR-trees
  • triconnectivity

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