The Complexity of Data Aggregation in Directed Networks

  • Fabian Kuhn
  • Rotem Oshman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6950)


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.


Span Tree Data Aggregation Sensitive Function Communication Complexity Directed Network 
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  1. 1.
    Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election and related problems (detailed summary). In: Proc. 19th ACM Symp. on Theory of Computing (STOC), pp. 230–240 (1987)Google Scholar
  2. 2.
    Chakrabarti, A., Regev, O.: An optimal lower bound on the communication complexity of gap-hamming-distance. In: Proc. 43rd ACM Symp. on Theory of Computing (STOC), pp. 51–60 (2011)Google Scholar
  3. 3.
    Frederickson, G.N., Lynch, N.A.: The impact of synchronous communication on the problem of electing a leader in a ring. In: Proc. 16th ACM Symp. on Theory of Computing (STOC), pp. 493–503 (1984)Google Scholar
  4. 4.
    Indyk, P., Woodruff, D.: Tight lower bounds for the distinct elements problem. In: Proc. 44th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 283–288 (October 2003)Google Scholar
  5. 5.
    Kalyanasundaram, B., Schnitger, G.: The probabilistic communication complexity of set intersection. SIAM J. Discrete Math. 5(4), 545–557 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 482–491 (2003)Google Scholar
  7. 7.
    Kuhn, F., Locher, T., Schmid, S.: Distributed computation of the mode. In: Proc. 27th ACM Symp. on Principles of Distributed Computing (PODC), pp. 15–24 (2008)Google Scholar
  8. 8.
    Kuhn, F., Locher, T., Wattenhofer, R.: Tight bounds for distributed selection. In: Proc. 19th ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 145–153 (2007)Google Scholar
  9. 9.
    Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: Proc. 42nd ACM Symp. on Theory of Computing (STOC), pp. 513–522 (2010)Google Scholar
  10. 10.
    Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  11. 11.
    Mosk-Aoyama, D., Shah, D.: Fast distributed algorithms for computing separable functions. IEEE Transactions on Information Theory 54(7), 2997–3007 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Negro, A., Santoro, N., Urrutia, J.: Efficient distributed selection with bounded messages. IEEE Trans. Parallel and Distributed Systems 8(4), 397–401 (1997)CrossRefGoogle Scholar
  13. 13.
    Patt-Shamir, B.: A note on efficient aggregate queries in sensor networks. In: Proc. 23rd ACM Symp. on Principles of Distributed Computing (PODC), pp. 283–289 (2004)Google Scholar
  14. 14.
    Razborov, A.A.: On the distributional complexity of disjointness. Theor. Comput. Sci. 106, 385–390 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Santoro, N., Scheutzow, M., Sidney, J.B.: On the expected complexity of distributed selection. J. Parallel and Distributed Computing 5(2), 194–203 (1988)CrossRefGoogle Scholar
  16. 16.
    Santoro, N., Sidney, J.B., Sidney, S.J.: A distributed selection algorithm and its expected communication complexity. Theoretical Computer Science 100(1), 185–204 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Shrira, L., Francez, N., Rodeh, M.: Distributed k-selection: From a sequential to a distributed algorithm. In: Proc. 2nd ACM Symp. on Principles of Distributed Computing (PODC), pp. 143–153 (1983)Google Scholar
  18. 18.
    Topkis, D.M.: Concurrent broadcast for information dissemination. IEEE Trans. Softw. Eng. 11, 1107–1112 (1985)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Fabian Kuhn
    • 1
  • Rotem Oshman
    • 2
  1. 1.University of LuganoSwitzerland
  2. 2.Massachusetts Institute of TechnologyUSA

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