@MISC{Henzinger92fullydynamic, author = {M. R. Henzinger}, title = {Fully Dynamic Biconnectivity in Graphs}, year = {1992} }

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Abstract

We present an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for insertions and for deletions is O(m 2=3 ), where m is the number of edges in the graph. Any query of the form "Are the vertices u and v biconnected?" can be answered in time O(1). This is the first sublinear algorithm for this problem. We can also output all articulation points separating any two vertices efficiently. If the input is a plane graph, the amortized running time for insertions and deletions drops to O( p n log n) and the query time is O(log 2 n), where n is the number of vertices in the graph. The best previously known solution takes time O(n 2=3 ) per update or query. 1 Introduction An undirected graph G = (V; E) is biconnected if there are at least two vertex--disjoint paths from each vertex to every other vertex. It is well known [1] that a graph G is n...