P. K. Agarwal, J. Basch, M. de Berg, L. J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. In Proc. 15th ACM Symp. on Computational Geometry, pages 247--254, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....or binary space partitions are not. To evaluate the efficiency of kinetic data structures that monitor non canonically defined discrete attributes of moving objects it is necessary to obtain lower bounds on the minimum amount of work required to maintain these attributes. Agarwal et al. [2] give first lower bounds on the number of changes to any BSP of moving segments or any Steiner triangulation of moving points in the plane. 2.2 Geometric Preliminaries Of particular relevance to the work of this thesis are the paper of Basch et al. 12] and its extension by Agarwal et al. 3] ....

....KDS is said to be efficient (see [40] if the number of events processed by the structure in the worst case is asymptotically of the same order as the number of external events, i.e. the number of changes to the discrete attribute one wishes to maintain. As already pointed out by Agarwal et al. in [2] the notion of efficiency in the case of data structures for collision detection is not clear, since there is no canonical discrete attribute against which to compare the performance of the KDS, i.e. it is not canonically defined what constitutes an external event. However it is somewhat natural ....

Pankaj K. Agarwal, Julien Basch, Mark de Berg, Leonidas J. Guibas, and John Her- shberger. Lower bounds for kinetic planar subdivisions. In Proc. 15th ACM Sympos. Comp. Geom., pages 247-254, 1999.

....failures) We also give a construction showing that for any constant c 1, there is a configuration of n points moving linearly on the real line so that any c approximate set of centers must change #(n times. Thus, even though an approximate clustering is not a canonical structure [1], we can claim efficiency for our method. To summarize, our clustering algorithm has a number of attractive properties: We can show that the clustering produced is an O(1) approximation. The clustering generated by the algorithm is smooth in the sense that a point s movement causes only ....

P. K. Agarwal, J. Basch, M. de Berg, L. J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. In Proc. 15th ACM Symp. on Computational Geometry, pages 247--254, 1999.

....number of external events. If this is the case then the KDS is called ecient. External events are only well de ned if the attribute being maintained is unique for any given con guration of objects. This is the case for convex hulls or closest pair, but not for BSPs. However, Agarwal et al. [1] have shown that there are con gurations of n moving segments, such that any BSPs must undergo n p n) changes during some smooth motion. BSPs have already been studied in a kinetic setting. For a set of n disjoint moving line segments in the plane, Agarwal et al. 3] present a kinetic BSP of ....

P.K. Agarwal, J. Basch, M. de Berg, L.J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. Discrete Comput. Geom., To appear.

....failures) We also give a construction showing that for any constant c 1, there is a configuration of n points moving linearly on the real line so that any c approximate set of centers must change #(n 2 c 2 ) times. Thus, even though an approximate clustering is not a canonical structure [2], we can claim efficiency for our method. Our clustering algorithm has a number of other attractive properties: We can show that the clustering produced is an O(1) approximation. The clustering generated by the algorithm is smooth in the sense that, degeneracies aside, clusters always ....

P. K. Agarwal, J. Basch, M. de Berg, L. J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. In Proc. 15thACMSymp.on Computational Geometry, pages 247--254, 1999.

....failures) We also give a construction showing that for any constant c 1, there is a configuration of n points moving linearly on the real line so that any c approximate set of centers must change## n 2 c 2 ) times. Thus, even though an approximate clustering is not a canonical structure [2], we can claim efficiency for our method. Our clustering algorithm has a number of other attractive properties: We can show that the clustering produced is an O(1) approximation with high probability during the entire history of a pseudo algebraic motion not only at a particular instant; ....

P. K. Agarwal, J. Basch, M. de Berg, L. J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. In Proc. 15th ACM Symp. on Computational Geometry, pages 247--254, 1999.

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