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CORR

2011

Springer

2011

Springer

Motivated by the desire to cope with data imprecision [8], we study methods for preprocessing a set of planar regions such that whenever we are given a set of points, each of which lies on a distinct region, we can compute a speciﬁed structure on these points more eﬃciently than in “standard settings” (that is, without preprocessing). In particular, we study the following problem. Given a set L of n lines in the plane, we wish to preprocess L such that later, upon receiving a set P of n points, each of which lies on a distinct line of L, we can construct the convex hull of P eﬃciently. We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(nα(n) log∗ n) expected time. The analysis applies almost verbatim when L is a set of line-segments, and yields the same asymptotic bounds.

Added |
19 Aug 2011 |

Updated |
19 Aug 2011 |

Type |
Journal |

Year |
2011 |

Where |
CORR |

Authors |
Esther Ezra, Wolfgang Mulzer |

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