Coresets in dynamic geometric data streams

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 + )-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( −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 p...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Gereon Frahling, Christian Sohler
• Keywords: Algorithms, Data Stream, Geometric Data Streams, Insert/delete Operation, STOC 2005