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Abstract: We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in R 2 or R 3 . Our planar structures are actually fitted for a more general class of objects --- (fi; ffi)-covered objects --- which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two... (Update)
Context of citations to this paper: More
.... for this case; previously, only a constant factor approximation result was known, with a simple algorithm described by Efrat et al. [11] (see Section 2) Our result thus extends Hochbaum and Maass by enlarging the class of objects with PTASs. 2 Preliminaries In the sequel,...
...of the k center problem in [1] implies a four approximation algorithm for the minimum piercing set problem for and L 2 . Efrat et al. [10] introduced a dynamic data structure based on segment trees which can be used for the piercing set problem. They presented a sequential...
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0.3: Geometric Range Searching and Its Relatives - Agarwal, Erickson (1997) (Correct)
0.2: On the Union of kappa-Curved Objects - Efrat, Katz (Correct)
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0.5: Range Searching and Point Location among Fat Objects - Overmars, van der Stappen (1994) (Correct)
0.4: On Piercing Sets of Objects - Katz, Nielsen (1996) (Correct)
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BibTeX entry: (Update)
A. Efrat, M.J. Katz, F. Nielsen, and M. Sharir, Dynamic Data Structures for Fat Objects and their Applications, Proceedings 5 Workshop on Algorithms and Data Structures, 1997 LNCS Vol. 1272, 297--306. http://citeseer.ist.psu.edu/efrat99dynamic.html More
@inproceedings{ efrat97dynamic,
author = "Alon Efrat and Matthew J. Katz and Franck Nielsen and Micha Sharir",
title = "Dynamic Data Structures for Fat Objects and Their Applications",
booktitle = "Workshop on Algorithms and Data Structures",
pages = "297-306",
year = "1997",
url = "citeseer.ist.psu.edu/efrat99dynamic.html" }
Citations (may not include all citations):214 Davenport Schinzel Sequences and Their Geometric Application.. - Sharir, Agarwal - 1995
139 A greedy heuristic for the set-covering problem (context) - Chvatal - 1979
133 Geometric Range Searching and Its Relatives - Agarwal, Erickson - 1998
127 Maintenance of configurations in the plane (context) - Overmars, van Leeuwen - 1981
69 Optimal packing and covering in the plane are NP-complete (context) - Fowler, Paterson et al. - 1981
60 Decomposable searching problems I: Static-to-dynamic transfo.. (context) - Bentley, Saxe - 1980
56 Range searching with efficient hierarchical cuttings (context) - Matousek - 1993
51 Almost optimal set covers in finite VCDimension (context) - Bronnimann, Goodrich - 1995
46 Dynamic half-space range reporting and its applications (context) - Agarwal, Matousek - 1995
41 Point location in fat subdivisions (context) - Overmars - 1992
40 Range searching and point location among fat objects - Overmars, van der Stappen - 1996
33 Vertical decomposition of shallow levels in 3-dimensional ar.. - Agarwal, Efrat et al. - 1995
33 Efficient hidden surface removal for objects with small unio.. - Katz, Overmars et al. - 1992
29 Ray shooting and other applications of spanning trees with l.. (context) - Agarwal - 1992
20 vertical ray shooting and 2-D point enclosure (context) - Katz - 1997
20 Computing depth orders and related problems - Agarwal, Katz et al. - 1995
16 Dynamic data structures for fat objects and their applicatio.. - Efrat, Katz et al. - 1999
16 Dynamic data structures for fat objects and their applicatio.. - Efrat, Katz et al. - 1997
14 The complexity of the free space for a robot moving amidst f.. - van der Stappen, Halperin et al. - 1993
8 Matching points into pairwise-disjoint noise regions: combin.. - Arkin, Kedem et al. - 1992
5 rd Workshop on Algorithms and Data Structures (context) - Clarkson, polytope et al. - 1993
2 301--310 (context) - Efrat, Itai et al. - 1996
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