TY - GEN

T1 - The complexity of data aggregation in directed networks

AU - Kuhn, Fabian

AU - Oshman, Rotem

PY - 2011

Y1 - 2011

N2 - 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 Ω(min{n, 1/ε2}/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 Õ(D+√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.

AB - 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 Ω(min{n, 1/ε2}/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 Õ(D+√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.

UR - http://www.scopus.com/inward/record.url?scp=80055039360&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24100-0_40

DO - 10.1007/978-3-642-24100-0_40

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AN - SCOPUS:80055039360

SN - 9783642240997

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 416

EP - 431

BT - Distributed Computing - 25th International Symposium, DISC 2011, Proceedings

T2 - 25th International Symposium on Distributed Computing, DISC 2011

Y2 - 20 September 2011 through 22 September 2011

ER -