Abstract
We 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) 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.
Original language | English |
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Journal | Theory of Computing Systems |
Volume | 68 |
Pages (from-to) | 1014–1048 |
ISSN | 1432-4350 |
DOIs | |
Publication status | Published - 2024 |
Keywords
- 2-connectivity
- Dynamic graphs
- Graph minors