@inproceedings{261bfa5f962b492fbfbe87cd6b473c35,

title = "Dynamic data structures for fat objects and their applications",

abstract = "We present several efficient dynamic data structures for point-enclosure queries involving convex fat objects in ℝ2 or ℝ3. 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 three problems: (i) Finding a perfect matching between a set of points and a set of convex fat objects. (ii) Finding a piercing set for a collection of convex fat objects, whose size is within a constant factor off the optimum size. (iii) Constructing a data structure for answering bounded-length segment- shooting queries: Given a set of fat objects in the plane as above, and a query oriented segment (formula presented) whose length is relatively short, find the first object hit by (formula presented).",

author = "Alon Efrat and Katz, {Matthew J.} and Franck Nielsen and Micha Sharir",

note = "Funding Information: I A preliminary version of this paper appeared as [14]. ∗Corresponding author. E-mail addresses: matya@cs.bgu.ac.il (M.J. Katz), alone@math.tau.ac.il (A. Efrat), nielsen@csl.sony.co.jp (F. Nielsen), sharir@math.tau.ac.il (M. Sharir). 1Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. 2Supported by NSF Grant CCR-97-32101, by a grant from the U.S.–Israeli Binational Science Foundation, by the ESPRIT IV LTR project No. 21957 (CGAL), and by the Hermann Minkowski–MINERVA Center for Geometry at Tel Aviv University. Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1997.; 5th International Workshop on Algorithms and Data Structures, WADS 1997 ; Conference date: 06-08-1997 Through 08-08-1997",

year = "1997",

doi = "10.1007/3-540-63307-3_69",

language = "English (US)",

isbn = "3540633073",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "297--306",

editor = "Frank Dehne and Jorg-Rudiger Sack and Andrew Rau-Chaplin and Roberto Tamassia",

booktitle = "Algorithms and Data Structures - 5th International Workshop, WADS 1997, Proceedings",

}