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arXiv · 1409.7240

Optimal decremental connectivity in planar graphs

Jakub Łącki·Piotr Sankowski
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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.

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Jakub Łącki, Piotr Sankowski. 2014-09-25. Optimal decremental connectivity in planar graphs. https://arxiv.org/abs/1409.7240

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