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Worst-Case Deterministic Fully-Dynamic Biconnectivity in Changeable Planar Embeddings

Authors Jacob Holm , Ivor van der Hoog , Eva Rotenberg

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • dynamic graphs
  • planarity
  • connectivity

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Abstract

We study dynamic planar graphs with n vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a planar graph, subject to connectivity and 2-vertex-connectivity (biconnectivity) queries between pairs of vertices. Whenever a query pair is connected and not biconnected, we find the first and last cutvertex separating them.
Additionally, we allow local changes to the embedding by flipping the embedding of a subgraph that is connected by at most two vertices to the rest of the graph.
We support all queries and updates in deterministic, worst-case, O(log² n) time, using an O(n)-sized data structure.

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Jacob Holm, Ivor van der Hoog, and Eva Rotenberg. Worst-Case Deterministic Fully-Dynamic Biconnectivity in Changeable Planar Embeddings. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SoCG.2023.40

Author Details

Jacob Holm
  • University of Copenhagen, Copenhagen, Denmark
Ivor van der Hoog
  • Technical University of Denmark, Lyngby, Denmark
Eva Rotenberg
  • Technical University of Denmark, Lyngby, Denmark

Funding

Ivor van der Hoog and Eva Rotenberg: Partially supported by Independent Research Fund Denmark grants 2020-2023 (9131- 00044B) "Dynamic Network Analysis".
  • Holm, Jacob: Partially supported by the VILLUM Foundation grant 16582, "BARC".
  • van der Hoog, Ivor: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 899987.

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