--- _id: '18787' 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. author: - first_name: Christian full_name: Sohler, Christian last_name: Sohler - first_name: Gereon full_name: Frahling, Gereon last_name: Frahling citation: ama: 'Sohler C, Frahling G. Coresets in Dynamic Geometric Data Streams. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC). ; 2005:209-217.' apa: Sohler, C., & Frahling, G. (2005). Coresets in Dynamic Geometric Data Streams. In Proceedings of the 37th ACM Symposium on Theory of Computing (STOC) (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 Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), 209–17, 2005. ieee: C. Sohler and G. Frahling, “Coresets in Dynamic Geometric Data Streams,” in Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), 2005, pp. 209–217. mla: Sohler, Christian, and Gereon Frahling. “Coresets in Dynamic Geometric Data Streams.” Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), 2005, pp. 209–17. short: 'C. Sohler, G. Frahling, in: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), 2005, pp. 209–217.' date_created: 2020-09-01T13:49:23Z date_updated: 2022-01-06T06:53:52Z department: - _id: '63' language: - iso: eng page: 209-217 publication: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC) status: public title: Coresets in Dynamic Geometric Data Streams type: conference user_id: '15415' year: '2005' ...