Core-Preserving Algorithms

We define a class of algorithms for constructing coresets of (geometric) data sets, and show that algorithms in this class can be dynamized eciently in the insertiononly (data stream) model. As a result, we show that for a set of points in fixed dimensions, additive and multiplicative "-coresets for the k-center problem can be maintained in O(1) and O(k) time respectively, using a data structure whose size is independent of the size of the input. We also provide a faster streaming algorithm for maintaining "-coresets for fat extent-related problems such as diameter and minimum enclosing ball.

[1]  Pankaj K. Agarwal,et al.  Practical methods for shape fitting and kinetic data structures using core sets , 2004, Symposium on Computational Geometry.

[2]  Pankaj K. Agarwal,et al.  Approximation Algorithms for k-Line Center , 2002, ESA.

[3]  Pankaj K. Agarwal,et al.  Maintaining approximate extent measures of moving points , 2001, SODA '01.

[4]  Pankaj K. Agarwal,et al.  Approximating extent measures of points , 2004, JACM.

[5]  R. Dudley.  Metric Entropy of Some Classes of Sets with Differentiable Boundaries , 1974 .

[6]  Timothy M. Chan.  Faster core-set constructions and data stream algorithms in fixed dimensions , 2004, SCG '04.

[7]  Matt Gibson,et al.  On clustering to minimize the sum of radii , 2008, SODA '08.

[8]  Sariel Har-Peled,et al.  No, Coreset, No Cry , 2004, FSTTCS.

[9]  Pankaj K. Agarwal,et al.  Exact and Approximation Algortihms for Clustering , 1997 .

[10]  Hamid Zarrabi-Zadeh.  An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions , 2010, Algorithmica.

[11]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.

[12]  Rina Panigrahy,et al.  Clustering to minimize the sum of cluster diameters , 2001, STOC '01.

[13]  Christian Sohler,et al.  Coresets in dynamic geometric data streams , 2005, STOC '05.

[14]  Sariel Har-Peled,et al.  On coresets for k-means and k-median clustering , 2004, STOC '04.

[15]  Sariel Har-Peled.  Clustering Motion , 2004, Discret. Comput. Geom..

[16]  Teofilo F. GONZALEZ,et al.  Clustering to Minimize the Maximum Intercluster Distance , 1985, Theor. Comput. Sci..

[17]  Pankaj K. Agarwal,et al.  A space-optimal data-stream algorithm for coresets in the plane , 2007, SCG '07.