An e-cient transformation for klee's measure problem in the streaming model

Gokarna Sharma, Costas Busch, Ramachandran Vaidyanathan, Suresh Rai, Jerry L. Trahan

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

Given a stream of rectangles over a discrete space, we consider the problem of computing the total number of distinct points covered by the rectangles. This can be seen as the discrete version of the two-dimensional Klee's measure problem for streaming inputs. We pro- vide an (ε δ)-Approximation for fat rectangles. For the case of arbitrary rectangles, we provide an O( p log U)- Approximation, where U is the total number of discrete points in the two-dimensional space. The time to pro- cess each rectangle, the total required space, and the time to answer a query for the total area are polylog- Arithmic in U. Our approximations are based on an eficient transformation technique which projects rect- Angle areas to one-dimensional ranges, and then uses a streaming algorithm for the Klee's measure problem in the one-dimensional space. The projection is determin- istic and to our knowledge it is the first approach of this kind which provides eficiency and accuracy trade-offs in the streaming model.

Original languageEnglish (US)
Pages83-88
Number of pages6
StatePublished - 2012
Externally publishedYes
Event24th Canadian Conference on Computational Geometry, CCCG 2012 - Charlottetown, PE, Canada
Duration: Aug 8 2012Aug 10 2012

Conference

Conference24th Canadian Conference on Computational Geometry, CCCG 2012
CountryCanada
CityCharlottetown, PE
Period8/8/128/10/12

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology

Fingerprint Dive into the research topics of 'An e-cient transformation for klee's measure problem in the streaming model'. Together they form a unique fingerprint.

Cite this