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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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)
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)
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)
Kalyanasundaram, B., Schnitger, G.: The probabilistic communication complexity of set intersection. SIAM J. Discrete Math. 5(4), 545–557 (1992)
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)
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)
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)
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)
Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, Cambridge (1997)
Mosk-Aoyama, D., Shah, D.: Fast distributed algorithms for computing separable functions. IEEE Transactions on Information Theory 54(7), 2997–3007 (2008)
Negro, A., Santoro, N., Urrutia, J.: Efficient distributed selection with bounded messages. IEEE Trans. Parallel and Distributed Systems 8(4), 397–401 (1997)
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)
Razborov, A.A.: On the distributional complexity of disjointness. Theor. Comput. Sci. 106, 385–390 (1992)
Santoro, N., Scheutzow, M., Sidney, J.B.: On the expected complexity of distributed selection. J. Parallel and Distributed Computing 5(2), 194–203 (1988)
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)
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)
Topkis, D.M.: Concurrent broadcast for information dissemination. IEEE Trans. Softw. Eng. 11, 1107–1112 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-24100-0_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24099-7
Online ISBN: 978-3-642-24100-0
eBook Packages: Computer ScienceComputer Science (R0)