Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Incremental clustering and dynamic information retrieval
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A randomized approximation scheme for metric MAX-CUT
Journal of Computer and System Sciences
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Finding Frequent Items in Data Streams
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Counting Distinct Elements in a Data Stream
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Better streaming algorithms for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Processing set expressions over continuous update streams
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
High-dimensional computational geometry
High-dimensional computational geometry
Deterministic sampling and range counting in geometric data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Range counting over multidimensional data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Adaptive sampling for geometric problems over data streams
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Sampling in dynamic data streams and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Summarizing and mining inverse distributions on data streams via dynamic inverse sampling
VLDB '05 Proceedings of the 31st international conference on Very large data bases
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A fast k-means implementation using coresets
Proceedings of the twenty-second annual symposium on Computational geometry
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Summarizing spatial data streams using ClusterHulls
Journal of Experimental Algorithmics (JEA)
Facility Location in Dynamic Geometric Data Streams
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Coresets and approximate clustering for Bregman divergences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Streaming Embeddings with Slack
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Small space representations for metric min-sum k-clustering and their applications
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Online and incremental algorithms for facility location
ACM SIGACT News
Property testing
Property testing
K-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
Memoryless facility location in one pass
ACM Transactions on Algorithms (TALG)
Width of points in the streaming model
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Memoryless facility location in one pass
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Streaming k-means on well-clusterable data
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
StreamKM++: A clustering algorithm for data streams
Journal of Experimental Algorithmics (JEA)
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A dynamic geometric data stream consists of a sequence of m insert/delete operations of points from the discrete space 1,…,Δd [26]. We develop streaming (1 + ε)-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 (ε-1, log m, log Δ) space and update time per insert/delete operation for constant k and dimension dHaving 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⁄ε)⁄ε)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⁄ε)O(1))) time. For MaxST and average distance we require poly(log n, ε-1) time and for MaxWM we require O(n3) time to do this.