In this paper, we initiate the study of the dynamic maintenance of
2-edge-connectivity relationships in directed graphs. We present an algorithm
that can update the 2-edge-connected blocks of a directed graph with n
vertices through a sequence of m edge insertions in a total of O(mn) time.
After each insertion, we can answer the following queries in asymptotically
optimal time: (i) Test in constant time if two query vertices v and w are
2-edge-connected. Moreover, if v and w are not 2-edge-connected, we can
produce in constant time a "witness" of this property, by exhibiting an edge
that is contained in all paths from v to w or in all paths from w to v.
(ii) Report in O(n) time all the 2-edge-connected blocks of G. To the
best of our knowledge, this is the first dynamic algorithm for 2-connectivity
problems on directed graphs, and it matches the best known bounds for simpler
problems, such as incremental transitive closure.Comment: Full version of paper presented at ICALP 201