Abstract
We present algorithms for maintaining the biconnected components of a planar graph undergoing repeated dynamic modifications, such as insertions and deletions of edges and vertices. We show how to test at any time whether two vertices belong to the same biconnected component, and how to insert and delete an edge in O(n2/3) time in the worst case, where n is the number of vertices in the graph. The data structure supports also insertions of new vertices and deletions of disconnected vertices in the same time bounds. This is the first sublinear-time algorithm known for this problem.
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