Decremental SPQR-trees for Planar Graphs

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, Eva Rotenberg, Michael Wagner
2018 European Symposium on Algorithms  
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. The previous best supported deletions and insertions in O( √ n ) time.
doi:10.4230/lipics.esa.2018.46 dblp:conf/esa/HolmIKLR18 fatcat:styzxed7dffvzlf5lp4zem25uu