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Optimal Decremental Connectivity in Planar Graphs

Authors Jakub Lacki, Piotr Sankowski

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Jakub Lacki
Piotr Sankowski

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Jakub Lacki and Piotr Sankowski. Optimal Decremental Connectivity in Planar Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 608-621, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.STACS.2015.608

Abstract

We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form 'Are vertices u and v connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n) time. This results improves over previously known O(n \log n) time algorithm.
Keywords
  • decremental connectivity
  • planar graphs
  • dynamic connectivity
  • algorithms

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