  In this work we address the question of efficiency of distributed computing
in anonymous, congested and highly dynamic and not-always-connected
networks/systems. More precisely, the system consists of an unknown number of
anonymous nodes with congestion on links and local computation. Links can
change arbitrarily from round to round, with only limitation that the union of
any T consecutive networks must form a temporarily connected (multi-)graph on
all nodes (knowledge of T is the only information the nodes require, otherwise
the communication would not be feasible). Nodes do not have any IDs, only some
number l of them have a bit distinguishing them from nodes without such a bit.
In each round a node can send and receive messages from its current neighbors.
Links and nodes are congested, in the sense that the length of messages and
local cache memory for local computation is (asymptotically) logarithmic.
  All-to-all communication is a fundamental principle in distributed computing
- it assumes that each node has an input message to be delivered to all other
nodes. Without loss of generality, the size of each input message is
logarithmic to fit in the link and node congestion assumption; otherwise, they
could be split in logarithmic batches and considered one-by-one. Because of
anonymity, each node needs to receive only a set of all input messages, each
accompanied by a number of initiating nodes (message multiplicity). We prove
that this task can be done in time polynomial in the (initially unknown) number
of nodes n and in the lower bound on the isoperimetric numbers of dynamically
evolving graphs. This allows to efficiently emulate a popular Congested Clique
model on top of Anonymous Dynamic Congested Systems (ADCS) with Opportunistic
Connectivity, even if the number of nodes may arbitrarily change in the
beginning of emulation.
