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A dynamic distributed data structure for top-\(k\) and \(k\)-select queries. (English) Zbl 1514.68046

Böckenhauer, Hans-Joachim (ed.) et al., Adventures between lower bounds and higher altitudes. Essays dedicated to Juraj Hromkovič on the occasion of his 60th birthday. Cham: Springer. Lect. Notes Comput. Sci. 11011, 311-329 (2018).
Summary: We consider a scenario where \(n\) sensor nodes observe streams of data. The nodes are connected to a central server whose task it is to compute some function over all data items observed by the nodes. Extending the capabilities of the distributed monitoring model from [G. Cormode et al., SODA 2008, 1076–1085 (2008; Zbl 1192.68080)], we allow, in addition to sending messages from the sensor nodes to the server, also broadcasts from the server to the sensor nodes.
In this paper, we address the problem of answering Top-\(k\) queries (report the \(k\) largest data items currently observed) and approximate \(k\)-Select queries (report an element with rank close to \(k)\). We present a communication-efficient dynamic data structure that supports these queries under updates of the data items arriving at the sensor nodes.
For the entire collection see [Zbl 1398.68015].

MSC:

68P05 Data structures

Citations:

Zbl 1192.68080
Full Text: DOI

References:

[1] Arackaparambil, C., Brody, J., Chakrabarti, A.: Functional monitoring without monotonicity. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 95-106. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02927-1_10 · Zbl 1248.68085 · doi:10.1007/978-3-642-02927-1_10
[2] Babcock, B., Olston, C.: Distributed Top-K monitoring. In: ACM SIGMOD International Conference on Management of Data, pp. 28-39. ACM (2003)
[3] Bemmann, P., et al.: Monitoring of domain-related problems in distributed data streams. In: Das, S., Tixeuil, S. (eds.) SIROCCO 2017. LNCS, vol. 10641, pp. 212-226. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72050-0_13 · Zbl 1496.68045 · doi:10.1007/978-3-319-72050-0_13
[4] Biermeier, F., Feldkord, B., Malatyali, M., Meyer auf der Heide, F.: A communication-efficient distributed data structure for Top-\(k\) and \(k\)-select queries. In: Solis-Oba, R., Fleischer, R. (eds.) WAOA 2017. LNCS, vol. 10787, pp. 285-300. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89441-6_21 · Zbl 1504.68042 · doi:10.1007/978-3-319-89441-6_21
[5] Cormode, G., Korn, F., Muthukrishnan, S., Srivastava, D.: Space-and time-efficient deterministic algorithms for biased quantiles over data streams. In: 25th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 263-272. ACM (2006)
[6] Cormode, G., Korn, F., Muthukrishnan, S., Srivastava, D.: Effective computation of biased quantiles over data streams. In: 21st International Conference on Data Engineering, pp. 20-31. IEEE (2005)
[7] Cormode, G., Muthukrishnan, S., Yi, K.: Algorithms for distributed functional monitoring. ACM Trans. Algorithms 7(2), 21 (2011) · Zbl 1295.68204 · doi:10.1145/1921659.1921667
[8] Cormode, G., Muthukrishnan, S., Yi, K.: Algorithms for distributed functional monitoring. In: 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1076-1085. Society for Industrial and Applied Mathematics (2008) · Zbl 1192.68080
[9] Mäcker, A., Malatyali, M., Meyer auf der Heide, F.: Online Top-\(k\)-position monitoring of distributed data streams. In: 29th International Parallel and Distributed Processing Symposium, pp. 357-364. IEEE (2015)
[10] Mäcker, A., Malatyali, M., Meyer auf der Heide, F.: On competitive algorithms for approximations of Top-\(k\)-position monitoring of distributed streams. In: 30th International Parallel and Distributed Processing Symposium, pp. 700-709. IEEE (2016)
[11] Madden, S., Franklin, M., Hellerstein, J., Hong, W.: The design of an acquisitional query processor for sensor networks. In: ACM SIGMOD International Conference on Management of Data, pp. 491-502. ACM (2003)
[12] Marberg, J., Gafni, E.: An optimal shout-echo algorithm for selection in distributed sets. In: 23rd Allerton Conference on Communication, Control, and Computing (1985)
[13] Muthukrishnan, S.: Data Streams: Algorithms and Applications. Now Publishers Inc. (2005) · Zbl 1128.68025
[14] Rotem, D., Santoro, N., Sidney, J.: Shout echo selection in distributed files. Networks 16(1), 77-86 (1986) · Zbl 0641.68030 · doi:10.1002/net.3230160108
[15] Yi, K., Zhang, Q.: Optimal tracking of distributed heavy hitters and quantiles. Algorithmica 65(1), 206-223 (2013) · Zbl 1259.68042 · doi:10.1007/s00453-011-9584-4
[16] Zengfeng, H., Yi, K., Zhang, Q.: Randomized algorithms for tracking distributed count, frequencies, and ranks. In: 31st ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 295-306. ACM (2012)
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