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In this work we address the question of efficiency of distributed computingin anonymous, congested and highly dynamic and not-always-connectednetworks/systems. More precisely, the system consists of an unknown number ofanonymous nodes with congestion on links and local computation. Links canchange arbitrarily from round to round, with only limitation that the union ofany T consecutive networks must form a temporarily connected (multi-)graph onall nodes (knowledge of T is the only information the nodes require, otherwisethe communication would not be feasible). Nodes do not have any IDs, only somenumber 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 andlocal 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 othernodes. Without loss of generality, the size of each input message islogarithmic to fit in the link and node congestion assumption; otherwise, theycould be split in logarithmic batches and considered one-by-one. Because ofanonymity, each node needs to receive only a set of all input messages, eachaccompanied by a number of initiating nodes (message multiplicity). We provethat this task can be done in time polynomial in the (initially unknown) numberof nodes n and in the lower bound on the isoperimetric numbers of dynamicallyevolving graphs. This allows to efficiently emulate a popular Congested Cliquemodel on top of Anonymous Dynamic Congested Systems (ADCS) with OpportunisticConnectivity, even if the number of nodes may arbitrarily change in thebeginning of emulation.

Efficient Distributed Computations in Anonymous Dynamic Congested Systems with Opportunistic Connectivity