Monitoring of Domain-Related Problems in Distributed Data Streams
Consider a network in which n distributed nodes are connected to a single server. Each node continuously observes a data stream consisting of one value per discrete time step. The server has to continuously monitor a given parameter defined over all information available at the distributed nodes. That is, in any time step t, it has to compute an output based on all values currently observed across all streams. To do so, nodes can send messages to the server and the server can broadcast messages to the nodes. The objective is the minimisation of communication while allowing the server to compute the desired output.
We consider monitoring problems related to the domain \(D_t\) defined to be the set of values observed by at least one node at time t. We provide randomised algorithms for monitoring \(D_t\), (approximations of) the size \(|D_t|\) and the frequencies of all members of \(D_t\). Besides worst-case bounds, we also obtain improved results when inputs are parameterised according to the similarity of observations between consecutive time steps. This parameterisation allows to exclude inputs with rapid and heavy changes, which usually lead to the worst-case bounds but might be rather artificial in certain scenarios.
- 1.Cormode, G., Muthukrishnan, S., Yi, K.: Algorithms for distributed functional monitoring. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 1076–1085. SIAM (2008)Google Scholar
- 3.Davis, S., Edmonds, J., Impagliazzo, R.: Online algorithms to minimize resource reallocations and network communication. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX/RANDOM -2006. LNCS, vol. 4110, pp. 104–115. Springer, Heidelberg (2006). https://doi.org/10.1007/11830924_12 CrossRefGoogle Scholar
- 4.Gibbons, P.B., Tirthapura, S.: Estimating simple functions on the union of data streams. In: Proceedings of the 13th annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 2001), pp. 281–291. ACM (2001)Google Scholar
- 5.Huang, Z., Yi, K., Zhang, Q.: Randomized algorithms for tracking distributed count, frequencies, and ranks. In: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2012), pp. 295–306. ACM (2012)Google Scholar
- 7.Mäcker, A., Malatyali, M., auf der Heide, F.M.: Online Top-k-position monitoring of distributed data streams. In: Proceedings of the 2015 IEEE International Parallel and Distributed Processing Symposium (IPDPS 2015), pp. 357–364. IEEE (2015)Google Scholar
- 8.Mäcker, A., Malatyali, M., auf der Heide, F.M.: On competitive algorithms for approximations of Top-k-position monitoring of distributed streams. In: Proceedings of the 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS 2016), pp. 700–709. IEEE (2016)Google Scholar
- 9.Woodruff, D.P., Zhang, Q.: Tight bounds for distributed functional monitoring. In: Proceedings of the 44th Symposium on Theory of Computing (STOC 2012), pp. 941–960. ACM (2012)Google Scholar