  Community search is a well-studied problem which, given a static graph and a
query set of vertices, requires to find a cohesive (or dense) subgraph
containing the query vertices. In this paper we study the problem of community
search in temporal dynamic networks. We adapt to the temporal setting the
notion of \emph{network inefficiency} which is based on the pairwise
shortest-path distance among all the vertices in a solution. For this purpose
we define the notion of \emph{shortest-fastest-path distance}: a linear
combination of the temporal and spatial dimensions governed by a user-defined
parameter. We thus define the \textsc{Minimum Temporal-Inefficiency Subgraph}
problem and show that it is \NPhard. We develop an algorithm which exploits a
careful transformation of the temporal network to a static directed and
weighted graph, and some recent approximation algorithm for finding the minimum
Directed Steiner Tree. We finally generalize our framework to the streaming
setting in which new snapshots of the temporal graph keep arriving continuously
and our goal is to produce a community search solution for the temporal graph
corresponding to a sliding time window.
