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A technique for adding range restrictions to generalized searching problems

Gupta, Prosenjit and Janardan, Ravi and Smid, Michiel

MPI-I-96-1-017. September 1996, 9 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.

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  AUTHOR = {Gupta, Prosenjit and Janardan, Ravi and Smid, Michiel},
  TITLE = {A technique for adding range restrictions to generalized searching problems},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-96-1-017},
  MONTH = {September},
  YEAR = {1996},
  ISSN = {0946-011X},