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(logn). In undirected networks of diameter D, many such problems can easily be solved in O(D) rounds, using O(logn)-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 ε-approximation to the size n of the network requires \(\Omega(\min \left\{n, 1/\epsilon ^2\right\} / B)\) rounds, even in networks of diameter 2. We also show that computing a sensitive function (e.g., minimum and maximum) requires \(\Omega(\sqrt{n/B})\) rounds in networks of diameter 2, provided that the diameter is not known in advance to be \(o(\sqrt{n/B})\). Our lower bounds are established by reduction from several well-known problems in communication complexity. On the positive side, we give a nearly optimal \(\tilde{O}(D + \sqrt{n/B})\)-round algorithm for computing simple sensitive functions using messages of size B = Ω(logN), where N is a loose upper bound on the size of the network and D is the diameter.
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Kuhn, F., Oshman, R. (2011). The Complexity of Data Aggregation in Directed Networks. In: Peleg, D. (eds) Distributed Computing. DISC 2011. Lecture Notes in Computer Science, vol 6950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24100-0_40
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DOI: https://doi.org/10.1007/978-3-642-24100-0_40
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