Efficient Distributed Computations in Anonymous Dynamic Congested Systems with Opportunistic Connectivity

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.