J. L. Bentley, D. F. Stanat, E. H. Williams, Jr.: The Complexity of FindingFixed-radiu: Near Neighbors, Information ProcesN ,Vol. 6, No. 6, pp. 209--212, December 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....fixed, and qu:L ranges arise many times; we are interested in preprocessing S in order to decrease the search time. Most of thepreviou: researches on this problem are restricted to the case where the shape of a qu:GS range R is orthogonal [1] half planar [6] circu:FF [3] 5] or spherical [2] [12] In this paper, on the other hand, we propose an algorithm for solving the two dimensional range search problem for a general shape of a qu:GG range R,by means of a simple techniqu: u:hni the Voronoi diagram. Fu:52= xMF5E a good average case performance is observed bynu:x2EGEL experiments. ....

....Based on the Voronoi Diag3i su:x L2 xM= weconstru:x the algorithm of the range search based on the Voronoi diagram. Similar to the side trip facility search, we firstly constru:x the Voronoi diagram of the inpu: point set S as the preprocess for this algorithm. we also prepare an array fA[1] A[2]; A[N ]g,each element has already been set False. It means that each inpu: point is not checked yet. In case that aninpu: point P n is checked, wesetA[n] True. As the preparatory step of eachqu:xF ,We prepare a qu:SF or a stack Q, which stores all of the inpu: points that has already been ....

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J. L. Bentley, D. F. Stanat, E. H. Williams, Jr.: The Complexity of FindingFixed-radiu: Near Neighbors, Information ProcesN ,Vol. 6, No. 6, pp. 209--212, December 1977.

....slower. Of course, when E is sparse our algorithm is far more efficient. Then I tried it against a Voronoi diagram computation. I believe it to be an interesting comparison for two reasons. First, no experimental result has been published for the previous fixed radius near neighbors algorithms [2, 7]. Second, Dickerson and Eppstein algorithm [7] starts by computing a Delaunay triangulation, which is equivalent to computing a Voronoi diagram. When k n, my program is about 100 times faster than an exact Voronoi diagram computation with CGAL [9] 4 Conclusion The main weakness of our ....

J. L. Bentley, D. F. Stanat, and E. H. William, Jr. The complexity of finding fixed-radius near neighbors. Inform. Process. Lett., 6:209--212, 1977.

....results will be published in a full version of this paper. Consider first the Fixed Radius Near Neighbors (FRNN ) problem: given a set P of n points in R d and a distance , find all pairs of points of P which are no further apart than under L t . Previous work on this problem includes [4, 9, 12, 26]. All of these (if applicable to high d) suffer from the dimensionality curse. We can solve the FRNN problem by simply removing portions of the CP k algorithm presented earlier. First, eliminate the approximation phase of the CP k algorithm, and instead use in place of ffi k;t . Second, out of ....

J. L. Bentley, D. F. Stanat, and E. H. William, Jr. The complexity of finding fixed-radius near neighbors. Inform. Process. Lett., 6:209--212, 1977.

....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 is the dimension and k the number of pairs reported. Algorithms for problem 1 have also been used by Salowe [21, 22] and Lenhof and Smid [17] as subroutines in parametric search methods for solving Problems 2 and 4. Problem 3 is a ....

J. Bentley, D. Stanat, and E. Williams Jr, "The Complexity of finding fixed-radius near neighbors," Information Processing Letters 6 (1977) 209-213.

....Triangulation Algorithms These results lead to the following greedy triangulation algorithm: 5.1 Algorithm 1 Step 1: Generate all plausible pairs with r 1 B. To do this, we generate all pairs of points separated by a distance of at most 2B=fl. This is the fixed radius near neighbors problem [2, 7]. In this case a bucketing algorithm by Bentley, Stanat, and Williams can solve the problem in time O(n m) where m is the number of pairs that lie within 2B=fl of one another. As each pair is generated, test to see if it is plausible using the method described below. Step 2: Generate all ....

J. Bentley, D. Stanat and E. William Jr., "The complexity of finding fixed-radius near neighbors." Information Processing Letters 6 (1977) 209--213.

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