Abstract
Computing over data streams is a recent phenomenon that is of growing interest in many areas of computer science, including databases, computer networks and theory of algorithms. In this scenario, it is assumed that the algorithm sees the elements of the input one-by-one in arbitrary order, and needs to compute a certain function of the input. However, it does not have enough memory to store the whole input. Therefore, it must maintain a “sketch” of the data. Designing a sketching method for a given problem is a novel and exciting challenge for algorithm design.
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References
Agarwal, P., Har-Peled, S.: Maintaining approximate extent measures of moving points. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (2001)
Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measure of points. Journal of the ACM
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. In: Proceedings of the Symposium on Theory of Computing, pp. 20–29 (1996)
Bagchi, A., Chaudhary, A., Eppstein, D., Goodrich, M.T.: Deterministic sampling and range counting in geometric data streams. In: Proceedings of the ACM Symposium on Computational Geometry (2004)
Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. In: Proceedings of the Symposium on Theory of Computing (1997)
Chan, T.: Faster core-set constructions and data stream algorithms in fixed dimensions. In: Proceedings of the ACM Symposium on Computational Geometry (2004)
Cormode, G., Muthukrishnan, S.: Radial histograms for spatial streams. DIMACS Tech Report (2003)
Charikar, M., O’Callaghan, L., Panigrahy, R.: Better streaming algorithms for clustering problems. In: Proceedings of the Symposium on Theory of Computing, pp. 30–39 (2003)
Frahling, G., Indyk, P., Sohler, C.: Estimating the weight of euclidean minimum spanning trees in data streams (Manuscript 2004)
Feigenbaum, J., Kannan, S., Zhang, J.: Computing diameter in the streaming and sliding-window models. Yale University Technical Report YALEU/DCS/TR-1245 (2002)
Flajolet, P., Martin, G.: Probabilistic counting algorithms for data base applications. Journal of Computer and System Sciences 31, 182–209 (1985)
Guha, S., Mishra, N., Motwani, R., O’Callaghan, L.: Clustering data streams. In: Proceedings of the Symposium on Theory of Computing (2001)
Har-Peled, S., Mazumdar, S.: Coresets for k-means and k-medians and their applications. In: Proceedings of the Symposium on Theory of Computing (2004)
Hershberger, J., Suri, S.: Adaptive sampling for geometric problems over data streams. In: Proceedings of the ACM Symposium on Principles of Database Systems (2004)
Indyk, P.: Tutorial: Algorithmic applications of low-distortion geometric embeddings. In: Proceedings of the Symposium on Foundations of Computer Science (2001)
Indyk, P.: Better algorithms for high-dimensional proximity problems via asymmetric embeddings. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (2003)
Indyk, P.: Algorithms for dynamic geometric problems over data streams. In: Proceedings of the Symposium on Theory of Computing (2004)
Meyerson, A.: Online facility location. In: Proceedings of the Symposium on Foundations of Computer Science, pp. 426–431 (2001)
Munro, J.I., Paterson, M.S.: Selection and sorting with limited storage. TCS 12 (1980)
Muthukrishnan, S., Strauss, M.: Maintenance of multidimensional histograms. In: Proceedings of the FSTTCS (2003)
Muthukrishnan, S.: Data streams: Algorithms and applications (invited talk at soda 2003) (2003), Available at http://athos.rutgers.edu/~muthu/stream-1-1.ps
Suri, S., Toth, C., Zhou, Y.: Range counting over multidimensional data streams. In: Proceedings of the ACM Symposium on Computational Geometry (2004)
Thaper, N., Guha, S., Indyk, P., Koudas, N.: Dynamic multidimensional histograms. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, SIGMOD (2002)
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Indyk, P. (2004). Streaming Algorithms for Geometric Problems. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_3
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DOI: https://doi.org/10.1007/978-3-540-30538-5_3
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