## 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 language | English (US) |
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Pages | 83-88 |

Number of pages | 6 |

State | Published - 2012 |

Externally published | Yes |

Event | 24th Canadian Conference on Computational Geometry, CCCG 2012 - Charlottetown, PE, Canada Duration: Aug 8 2012 → Aug 10 2012 |

### Conference

Conference | 24th Canadian Conference on Computational Geometry, CCCG 2012 |
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Country/Territory | Canada |

City | Charlottetown, PE |

Period | 8/8/12 → 8/10/12 |

## ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology