Unions of Onions: Preprocessing Imprecise
نویسندگان
چکیده
Let D be a set of n pairwise disjoint unit disks in the plane. 8 We describe how to build a data structure for D so that for any point 9 set P containing exactly one point from each disk, we can quickly find 10 the onion decomposition (convex layers) of P . 11 Our data structure can be built in O(n logn) time and has linear size. 12 Given P , we can find its onion decomposition in O(n log k) time, where 13 k is the number of layers. We also provide a matching lower bound. 14 Our solution is based on a recursive space decomposition, combined with 15 a fast algorithm to compute the union of two disjoint onion decomposi16 tions. 17
منابع مشابه
Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition
4 Let D be a set of n pairwise disjoint unit disks in the plane. We describe how to build a data structure for D so that 5 for any point set P containing exactly one point from each disk, we can quickly find the onion decomposition (convex 6 layers) of P . 7 Our data structure can be built in O(n logn) time and has linear size. Given P , we can find its onion decomposition 8 in O(n log k) time,...
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