Offline Dynamic Higher Connectivity.

We give the first $O(tlog{t})$ time algorithm for processing a given sequence of $t$ edge updates and 3-vertex/edge connectivity queries in an undirected unweighted graph. Our approach builds upon a method by Eppstein (1994) that reduces graphs to smaller equivalents on a set of key vertices. It also leads to algorithms for offline 2-vertex/edge connectivity whose performances match those from Kaczmarz and Lacki (2015).