J. Vahrenhold and K. H. Hinrichs. Planar point location for large data sets: To seek or not to seek. In Proc. Workshop on Algorithm Engineering, LNCS 1982.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....grant INT 0129182. Email: large cs.duke.edu. Supported in part by the National Science Foundation through grant CCR 9984099. Email: adanner cs.duke.edu. bucket approach, Vahrenhold and Hinrichs developed a simple and practically e#cient, but theoretically nonoptimal, heuristic structure [24]. In this paper, we show that a point location structure based on a persistent B tree is e#cient both in theory and practice; the structure obtains the theoretical optimal bounds and our experimental investigation shows that, for a wide range of real world GIS data, it uses fewer I Os to answer a ....

....Goodrich et al. 17] developed an optimal static point location structure using linear space and answering a query in O(log B N) I Os. Agarwal et al. 1] and Arge and Vahrenhold [8] developed dynamic structures. Several structures for answering a batch of queries have also been developed [17, 9, 13, 24]. Refer to [4] for a survey. While these structures are all theoretically I O e#cient, they are all relatively complicated and consequently none of them have been implemented. Based on an internal memory bucket approach [15] Vahrenhold and Hinrichs therefore developed a simple but non optimal ....

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J. Vahrenhold and K. H. Hinrichs. Planar point location for large data sets: To seek or not to seek. In Proc. Workshop on Algorithm Engineering, LNCS 1982.

.... memory, a lot of work has been done on this problem see e.g. the survey by Snoeyink [140] Goodrich et al. 86] described the first query optimal O(log B N) I O static solution to the problem, and several structures which can answer a batch of queries I O efficiently have also been developed [86, 29, 25, 65, 143]. Recently, progress has been made in the development of I O efficient dynamic point location structures. In the dynamic version of the problem one can change the subdivision dynamically (insert and delete edges and vertices) Based on the external interval tree structure and ideas also utilized ....

J. Vahrenhold and K. H. Hinrichs. Planar point-location for large data sets: To seek or not to seek. In Proc. Workshop on Algorithm Engineering, 2000.

....Publications Dept, ACM Inc. 1515 Broadway, New York, NY 10036 USA, fax 1 (212) 869 0481, or permissions acm.org. none of them have been implemented. Based on a bucket approach, Vahrenhold and Hinrichs developed a simple and practically ecient, but theoretically non optimal, heuristic structure [24]. In this paper, we show that a point location structure based on a persistent B tree is ecient both in theory and practice; the structure obtains the theoretical optimal bounds and our experimental investigation shows that, for a wide range of real world GIS data, it uses fewer I Os to answer a ....

....is often called partial persistence as opposed to full persistence where updates can be performed on any previous version. Based on an internal memory bucket approach [15] Vahrenhold and Hinrichs therefore developed a simple but non optimal heuristic structure, which performs well in practice [24]. The main idea in this structure is to impose a grid on the segments de ning the subdivision and store each segment in a bucket corresponding to each grid cell it intersects. The grid is constructed such that for certain kinds of nice data , each segment is stored in O(1) buckets (such that ....

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J. Vahrenhold and K. H. Hinrichs. Planar point location for large data sets: To seek or not to seek. In Proc. Workshop on Algorithm Engineering, LNCS 1982.

....and CAREER grant CCR 9984099. Email: large cs.duke.edu. Part of this work was done while visiting Duke University. Email: jan math.uni muenster.de. memory [7, 11, 12, 17, 20, 24] Only a few results are known for I O ecient point location when the subdivision is stored in external memory [1, 5, 14, 18, 27]. In this paper, we develop the rst space and I O ecient dynamic data structure for planar point location in general subdivisions. Previously such a structure was only known for the case of a monotone subdivision [1] 1.1 Previous results In internal memory, Edelsbrunner et al. 16] ....

....al. 5] extended the batched result to general subdivisions (see also [14] and Arge et al. 4] to an o line dynamic setting in which a sequence of queries and updates are given in advance and all the queries should be answered as the sequence of operations is performed. Vahrenhold and Hinrichs [27] considered the problem under some practical assumptions about the input data. The only known dynamic structure, recently proposed by Agarwal et al. 1] is restricted to monotone subdivisions. The linear space (O(N=B) A polygon is called monotone in direction if any line in direction =2 ....

J. Vahrenhold and K. H. Hinrichs. Planar point location for large data sets: To seek or not to seek. In Proc. Workshop on Algorithm Engineering, LNCS 1982.

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