  The Massive Parallel Computing (MPC) model gained popularity during the last
decade and it is now seen as the standard model for processing large scale
data. One significant shortcoming of the model is that it assumes to work on
static datasets while, in practice, real-world datasets evolve continuously. To
overcome this issue, in this paper we initiate the study of dynamic algorithms
in the MPC model.
  We first discuss the main requirements for a dynamic parallel model and we
show how to adapt the classic MPC model to capture them. Then we analyze the
connection between classic dynamic algorithms and dynamic algorithms in the MPC
model. Finally, we provide new efficient dynamic MPC algorithms for a variety
of fundamental graph problems, including connectivity, minimum spanning tree
and matching.
