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Decremental SPQR-trees for Planar Graphs


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 Ω(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. This is an exponential improvement over the previous best bound of O(√ n) that has stood for over 20 years. In addition, the previous data structures only supported edge deletions.
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hal-01925961 , version 1 (18-11-2018)



Jacob Holm, Giuseppe F Italiano, Adam Karczmarz, Jakub Łącki, Eva Rotenberg. Decremental SPQR-trees for Planar Graphs. European Symposium on Algorithms, 2018, Helsinki, Finland. ⟨hal-01925961⟩


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