Optimal Decremental Connectivity in Planar Graphs
Jakub Łącki, Piotr Sankowski · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2015
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.