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In this paper we study two related iterative randomized algorithms fordistributed computation of averages. The first one is the recently proposedBroadcast Gossip Algorithm, in which at each iteration one randomly selectednode broadcasts its own state to its neighbors. The second algorithm is a novelde-synchronized version of the previous one, in which at each iteration everynode is allowed to broadcast, with a given probability: hence this algorithm isaffected by interference among messages. Both algorithms are proved toconverge, and their performance is evaluated in terms of rate of convergenceand asymptotical error: focusing on the behavior for large networks, wehighlight the role of topology and design parameters on the performance.Namely, we show that on fully-connected graphs the rate is bounded away fromone, whereas the asymptotical error is bounded away from zero. On the contrary,on a wide class of locally-connected graphs, the rate goes to one and theasymptotical error goes to zero, as the size of the network grows larger.

Broadcast gossip averaging algorithms: interference and asymptotical error in large networks