A Dynamic Data Structure for Maintaining Disjoint Paths Information in Digraphs

摘要

In this paper we present the first dynamic data structure for testing - in constant time - the existence of two edge- or quasi-internally vertex-disjoint paths p_1 from s to t_1 and p_2 from s to t_2 for any three given vertices s, t_1, and t_2 of a digraph. By quasi-internally vertex-disjoint we mean that no inner vertex of p_1 appears on p_2 and vice versa. Moreover, for two vertices s and t, the data structure supports the output of all vertices and all edges whose removal would disconnect s and t in a time linear in the size of the output. The update operations consist of edge insertions and edge deletions, where the implementation of edge deletions will be given only in the full version of this paper. The update time after an edge deletion is competitive with the reconstruction of a static data structure for testing the existence of disjoint paths in constant time, whereas our data structure performs much better in the case of edge insertions.