Abstract. We study problems of data aggregation, such as approximate counting and computing the minimum input value, in synchronous directed networks with bounded message bandwidth B = Ω(log n). In undirected networks of diameter D, many such problems can easily be solved in O(D) rounds, using O(log n)-size messages. We show that for directed networks this is not the case: when the bandwidth B is small, several classical data aggregation problems have a time complexity that depends polynomially on the size of the network, even when the diameter of the network is constant. We show that computing an ǫ-approximation to the size n of the network requires Ω(min n, 1/ǫ 2 /B) rounds, even in networks of diameter 2. We also show that computing a sensitive function (e.g., minimum and maximum) requires Ω( n/B) rounds in networks of diameter 2, provided that the diameter is not known in advance to be o( n/B). Our lower bounds are established by reduction from several well-known problems in communication complexity. On the positive side, we give a nearly optimal O(D + n/B)-round algorithm for computing simple sensitive functions using messages of size B = Ω(log N ), where N is a loose upper bound on the size of the network and D is the diameter.
Data aggregation problems have also been studied in directed networks REF .
The complexity of data aggregation in directed networks
Distributed Computing: 25th International Symposium on Distributed Computing (DISC 2011
Mathematics Computer Science