{"date_created":"2020-09-01T13:49:23Z","status":"public","_id":"18787","user_id":"15415","author":[{"first_name":"Christian","full_name":"Sohler, Christian","last_name":"Sohler"},{"last_name":"Frahling","full_name":"Frahling, Gereon","first_name":"Gereon"}],"year":"2005","type":"conference","citation":{"short":"C. Sohler, G. Frahling, in: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), 2005, pp. 209–217.","ama":"Sohler C, Frahling G. Coresets in Dynamic Geometric Data Streams. In: <i>Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)</i>. ; 2005:209-217.","ieee":"C. Sohler and G. Frahling, “Coresets in Dynamic Geometric Data Streams,” in <i>Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)</i>, 2005, pp. 209–217.","bibtex":"@inproceedings{Sohler_Frahling_2005, title={Coresets in Dynamic Geometric Data Streams}, booktitle={Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)}, author={Sohler, Christian and Frahling, Gereon}, year={2005}, pages={209–217} }","chicago":"Sohler, Christian, and Gereon Frahling. “Coresets in Dynamic Geometric Data Streams.” In <i>Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)</i>, 209–17, 2005.","mla":"Sohler, Christian, and Gereon Frahling. “Coresets in Dynamic Geometric Data Streams.” <i>Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)</i>, 2005, pp. 209–17.","apa":"Sohler, C., &#38; Frahling, G. (2005). Coresets in Dynamic Geometric Data Streams. In <i>Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)</i> (pp. 209–217)."},"department":[{"_id":"63"}],"language":[{"iso":"eng"}],"page":"209-217","date_updated":"2022-01-06T06:53:52Z","title":"Coresets in Dynamic Geometric Data Streams","abstract":[{"lang":"eng","text":"A dynamic geometric data stream consists of a sequence of m insert/delete operations of points from the discrete space {1,..., ∆} d [26]. We develop streaming (1 + ɛ)-approximation algorithms for k-median, k-means, MaxCut, maximum weighted matching (MaxWM), maximum travelling salesperson (MaxTSP), maximum spanning tree (MaxST), and average distance over dynamic geometric data streams. Our algorithms maintain a small weighted set of points (a coreset) that approximates with probability 2/3 the current point set with respect to the considered problem during the m insert/delete operations of the data stream. They use poly(ɛ −1, log m, log ∆) space and update time per insert/delete operation for constant k and dimension d. Having a coreset one only needs a fast approximation algorithm for the weighted problem to compute a solution quickly. In fact, even an exponential algorithm is sometimes feasible as its running time may still be polynomial in n. For example one can compute in poly(log n, exp(O((1+log(1/ɛ)/ɛ) d−1))) time a solution to k-median and k-means [21] where n is the size of the current point set and k and d are constants. Finding an implicit solution to MaxCut can be done in poly(log n, exp((1/ɛ) O(1))) time. For MaxST and average distance we require poly(log n, ɛ −1) time and for MaxWM we require O(n 3) time to do this."}],"publication":"Proceedings of the 37th ACM Symposium on Theory of Computing (STOC)"}