M. Dickerson and R. L. Drysdale, Fixed radius search problems for points and segments, Inform. Process. Lett., 35 (1990), pp. 269273.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the complexity of the above construction. The k i 0 helicoidal vol 16 J. D. BOISSONNAT, O. DEVILLERS, AND S. LAZARD umes H i that intersect C i 0 can be found in O(k i 0 ) amortized time once the Delaunay triangulation of the footholds has been computed, which can be done in O(n log n) time [5, 17]. By Proposition 4.9, the upper and lower envelopes can be computed in O(k i 0 log k i 0 ) time using O(k i 0 ff(k i 0 ) space where ff is the pseudo inverse of the Ackerman s function [6] Also by Proposition 4.9, the union of Omega 1 and Omega 2 can be done in linear time in the size of the ....

....of (F) if and only if s i 0 is a vertex of the convex hull of the footholds reachable from s i 0 . The k 0 i 0 footholds contained in the disk of radius R centered at s i 0 can be found in O(k 0 i 0 ) amortized time because we have already computed the Delaunay triangulation of the footholds [5, 17]. Thus, we can decide if s i 0 is a vertex of the convex hull of these k 0 i 0 footholds in O(k 0 i 0 ) time and space. When s i 0 is a vertex of the convex hull, we can also nd the two edges of the convex hull adjacent to s i 0 in O(k 0 i 0 ) time and space. As the sum of the k 0 i for ....

M. Dickerson and R. L. Drysdale, Fixed radius search problems for points and segments, Inform. Process. Lett., 35 (1990), pp. 269273.

....the union of the regions of Omega 2 . Let us analyze the complexity of the above construction. The k i 0 helicoidal volumes H i that intersect C i 0 can be found in O(k i 0 ) amortized time once the Delaunay triangulation of the footholds has been computed which can be done in O(n log n) time [DD90, Tur91]. Since two curves ae i and ae j intersect each other at most once (Propositions 12, 13, 15) the upper and lower envelopes can be computed in O(k i 0 log k i 0 ) time and O(k i 0 ff(k i 0 ) space where ff is the pseudo inverse of the Ackerman s function [Her89] The union of Omega 1 and Omega ....

....straight edges ffi(F ) if and only if s i 0 is a vertex of the convex hull of the footholds reachable from s i 0 . The k 0 i 0 footholds contained in the disk D(s i 0 ; R) can be found in O(k 0 i 0 ) amortized time because we have already computed the Delaunay triangulation of the footholds [DD90, Tur91]. Thus, we can decide if s i 0 is a vertex of the convex hull of these k 0 i 0 footholds in O(k 0 i 0 ) time and space. When s i 0 is a vertex of the convex hull, we can also nd the two edges of the convex hull adjacent to s i 0 in O(k 0 i 0 ) time and space. As the sum of the k 0 i for ....

M. Dickerson and R. L. Drysdale. Fixed radius search problems for points and segments. Inform. Process. Lett., 35:269273, 1990.

....1 kisknown in advance and the pairs are not necessarily enumerated in order, and also an easier version of Problem 2 where we do not require the neighbors to be enumerated in order by distance. The algorithms we present in this paper extend the recent planar results of Dickerson and Drysdale [9] and Dickerson, Drysdale, and Sack [11] to higher dimensions by making use of the results of Bern, Eppstein, and Gilbert [3] on provably good mesh generation. Bern, et al. showed how for a set S of points in arbitrary dimension, a superset S # of S could be found in O(n log n) time so that the ....

....expect there to be a faster algorithm for selection than for the enumeration problem which may have large output size. That is, it would be nice to have an algorithm for selection whose running time is independent of k. Problem 1 has also received considerable attention. It was pointed out in [9] that the fixed radius search arises in many situations when we have a density restriction no more than m pairs of points may lie within a given distance of each other. The problem was originally solved by Bentley, Stanat, and Williams [5] in worst case time O(3 d dn log n 3 d k) where d ....

M. Dickerson and R. L. Drysdale, "Fixed radius search problem for points and segments", Information Processing Letters 35 (1990) 269--273.

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