Fully dynamic biconnectivity in graphs

The author presents an algorithm for maintaining the bi-connected 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/sup 2/3/), where m is the number of edges in the graph. Each 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. If the input is a planar embedded graph, the amortized running time for insertions and deletions drops to O( square root nlogn) and the worst case query time is O((logn)/sup 2/), where n is the number of vertices in the graph. The best previously known solution takes time O(n/sup 2/3/) per update or query.<<ETX>>