Abstract
AbstractWe present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in $$O(m+n)$$
O
(
m
+
n
)
time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in worst-case O(1) time. In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case O(1) time. As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, including planar graphs and other minor free graphs.
Funder
villum fonden
det frie forskningsråd
natur og univers, det frie forskningsråd
Publisher
Springer Science and Business Media LLC
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