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

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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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