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CORR
2011
Springer

Convex Hull of Imprecise Points in o(n \log{n}) Time after Preprocessing

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Convex Hull of Imprecise Points in o(n \log{n}) Time after Preprocessing
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.
Esther Ezra, Wolfgang Mulzer
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors Esther Ezra, Wolfgang Mulzer
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