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A technique for adding range restrictions to generalized searching problems

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44551

Gupta,  Prosenjit
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45509

Smid,  Michiel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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1996-1-017
(Any fulltext), 10KB

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Citation

Gupta, P., Janardan, R., & Smid, M.(1996). A technique for adding range restrictions to generalized searching problems (MPI-I-1996-1-017). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A15E-F
Abstract
In a generalized searching problem, a set $S$ of $n$ colored geometric objects has to be stored in a data structure, such that for any given query object $q$, the distinct colors of the objects of $S$ intersected by $q$ can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp.\ fat triangles) with a fat triangle (resp.\ point). For both problems, a data structure is obtained having size $O(n^{1+\epsilon})$ and query time $O((\log n)^2 + C)$. Here, $C$ denotes the number of colors reported by the query, and $\epsilon$ is an arbitrarily small positive constant.