Article,
Good r-divisions Imply Optimal Amortized Decremental Biconnectivity
Affiliations
- [1] University of Copenhagen [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD];
- [2] Technical University of Denmark [NORA names: DTU Technical University of Denmark; University; Denmark; Europe, EU; Nordic; OECD]
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.
Keywords
2-connectivity,
Dynamic graphs,
Graph minors