L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. European Symp. Algorithms, LNCS 979, pages 295--310, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....designer to ignore the critical issue of partitioning and allocating a large data set across multiple disk drives so as to balance disk loads. Numerous algorithms have been developed using the parallel disk model (PDM) from sorting and permutation primitives to computational geometry [SN96, AVV97] Nonetheless, the parallel disk model still seems limited in that it does not model the use of caching. Several models have been developed for dealing with multi level memory hierarchies. One is the Uniform Memory Hierarchy (UMH) model [VN93] The model can be adjusted using two integer ....

Lars Arge, Darren Erik Vengro#, and Je#rey Scott Vitter. External-memory algorithms for processing line segments in geographic information systems. Algorithmica, 1997. To appear.

....requires Omega Gamma N log N) comparisons in the comparison model, requires Omega Gamma N B log M B N B ) I Os in 1 log M B N B is defined to mean maxf1; log M B M B g. the PDM model. EM algorithms have been proposed for a number of problems arising in computational geometry [7, 5, 15, 25], geographical information systems [7, 36] and graphs [4, 11, 26, 34] Over the last few years, comprehensive computing and cost models, that incorporate multiple disks and multiple processors have been proposed [13, 17, 20, 27] Several suggestions have been made regarding the simulation of ....

....the comparison model, requires Omega Gamma N B log M B N B ) I Os in 1 log M B N B is defined to mean maxf1; log M B M B g. the PDM model. EM algorithms have been proposed for a number of problems arising in computational geometry [7, 5, 15, 25] geographical information systems [7, 36], and graphs [4, 11, 26, 34] Over the last few years, comprehensive computing and cost models, that incorporate multiple disks and multiple processors have been proposed [13, 17, 20, 27] Several suggestions have been made regarding the simulation of parallel algorithms as EM algorithms. This ....

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Arge, L., Vengroff, D. E., and Vitter, J. S. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979 (1995), pp. 295--310. A complete version (to appear in special issue of Algorithmica) appears as BRICS technical report RS-96-12, University of Aarhus.

.... of orthogonal line segments, answering range queries in the plane, nding all nearest neighbors for a set of N points in the plane, dominance problems, and other geometric problems in the plane are discussed in [2, 3, 7, 13, 20] General line segment intersection problems have been studied in [6]. For lower bounds on computational geometry problems in EM see [5] See [4] for bu er trees, priority queues, and their applications. Overview. In Sect. 2, we discuss our solution to the batched range counting problem. In Sect. 3, we use the solution for a special case of this problem to compute ....

....follows the framework of [11] However, we need to change the plane sweep substantially, in order to perform it I O eciently. For this purpose, we have to prove some new properties of conical Voronoi diagrams. The I Ocomplexity of our algorithm becomes O(sort(N) if the endpoint dominance problem [6] can be solved in O(sort(N) I Os. The algorithm iterates over all cones c 2 C and computes the conical Voronoi diagram CVD c (O) Fig. 1a) consisting of Voronoi regions V x , x 2 P . For each such region V x and each point p 2 V x , x is the closest visible obstacle vertex in c(p) Thus, for all ....

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L. Arge, D. E. Vengro, J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. Proc. ESA, pp. 295-310, 1995.

....= M=B and k = K=B. In fact, the first term derives from the optimal I O cost for sorting the N segments of S [1] whereas the latter term derives from the cost due to the storage of the produced output on the disk. No I O optimal algorithm is known. The best known algorithms are due to Arge et al. [3]. They solve the segment intersection problem (their algorithm does not compute the trapezoidal decomposition) in sub optimal O( n k) log m n) I Os, and they show how to compute the trapezoidal decomposition induced by a set of N non intersecting segments in optimal O(n log m n) I Os. In this ....

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, 295--310, 1995.

....n = N=B, m = M=B, and k = K=B. Goodrich et al. 16] suggested a batched planar point location algorithm for monotone subdivisions using persistent B trees that needs O ; n K=B)log m n Delta I O operations for preprocessing N segments and locating K query points. Arge, Vengroff, and Vitter [7] perform batched planar point location of K points among N segments in O ; n K=B) log m n Delta I O operations using the extended external segment tree. The algorithm relies on an external memory variant of fractional cascading [9] and thus the practical realization of their algorithm is ....

....set which causes a single bucket to overflow. However, if there is an overfull bucket, we can detect it during preprocessing, and can further preprocess the bucket (or rather, the column containing it) with an optimal external memory point location algorithm, e.g. the algorithm of Arge et al. [7]. We omit details and only note that this additional preprocessing does not asymptotically increase the overall preprocessing time [26] The costs for locating K points are composed of the I O operations spent on sorting and on loading the buckets. The number of buckets to be loaded depends on ....

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L. Arge, D. Vengroff, and J. Vitter. External-memory algorithms for processing line segments in geographic information systems. Proc. 3rdAnnual European Symp. Algorithms, LNCS 979, 295--310. 1995.

....Email: large cs.duke.edu y Westfalische Wilhelms Universitat, Institut fur Informatik, 48149 Munster, Germany.Part of this work was done while visiting DukeUniversity. Email: jan math.uni muenster.de known for I O efficient point location when the subdivision is stored in external memory [1, 6, 15, 18, 27]. In this paper, we develop the first space and I O efficient dynamic data structure for planar point location in general subdivisions. Previously such a structure was only known for the case of a monotone 1 subdivision [1] 1.1 Previous results In internal memory, Edelsbrunner and Maurer ....

....et al. 18] designed a static data structure using O(N=B) space to store a monotone subdivision so that a query can be answered in optimal O(log B N ) I Os. They also developed a structure for answering a batchofK point location queries in optimal O( N K) B) log M=B N ) I Os. Arge et al. [6] extended the batched result to general subdivisions (see also [15] and Arge et al. 5] to an off 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 are performed. Vahrenhold and Hinrichs [27] ....

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L. Arge, D. E. Vengroff, and J. S. Vitter. Externalmemory algorithms for processing line segments in geographic information systems. Algorithmica (to appear in special issues on Geographical Information Systems). Extended abstract appears in Proc. of Third European Symposium on Algorithms, 1995.

....results in this area have been obtained in [17, 32] Also, Kanellakis et al. 21] and Ramaswamy and Subramanian [26, 27] give efficient data structures for performing range searching in external memory. Very recently, a new data structure called buffer tree and its applications are given in [2, 3], and an external memory version of the directed topology tree ( 18] called topology B tree is given in [9] For excellent examples of experimental work in computational geometry, see Bentley [5, 6, 7, 8] As for experimental work on I O efficient computation, very recently Vengroff has built an ....

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. Manuscript, 1995.

....sweeping can also be applied to finding pairwise rectangle intersections and some other problems. 2.2 Red Blue Line Segment Intersection Given a set of non intersecting red segments and a set of non intersecting blue segments, report the intersections between red and blue segments. Arge et al. AVV95] were the first to solve this problem I O optimally in O(n log m n k) They used an I O optimal algorithm to sort segments according to the aboveness relation via an external memory segment tree and employed a variant of distribution sweeping with a branching factor of p m. 2.3 General Line ....

....to the aboveness relation via an external memory segment tree and employed a variant of distribution sweeping with a branching factor of p m. 2. 3 General Line Segment Intersection A first step to compute the intersections of arbitrary line segments I O efficiently was taken by Arge et al. AVV95] They presented a very involved algorithm using an extended external segment tree and a variant of distribution sweeping to achieve an I O bound of O( n k) log m n) Crauser et al. CFM 98] used the important techinque of randomized incremental construction with gradations to obtain an ....

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L. Arge, D.E. Vengroff, and J.S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In 3rd European Symposiom on Algorithms, 1995. 7

....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 ....

L. Arge, D. E. Vengro#, and J. S. Vitter. Externalmemory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295--310, 1995. To appear in special issues of Algorithmica on Geographical Information Systems.

No context found.

L. Arge, D. E. Vengro, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295-310, 1995. To appear in special issues of Algorithmica on Geographical Information Systems.

....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] ....

....et al. 18] designed a static data structure using O(N=B) space to store a monotone subdivision so that a query can be answered in optimal O(log B N) I Os. They also developed a structure for answering a batch of K point location queries in optimal O( N K) B) log M=B N) I Os. Arge et 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] ....

[Article contains additional citation context not shown here]

L. Arge, D. E. Vengro, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295-310, 1995. To appear in special issues of Algorithmica on Geographical Information Systems.

....need to increase the fanout of the base tree to decrease its height to O(log B N ) This creates several problems. The main idea behind our successful externalization of the structure, as compared with previous attempts [15, 38] is that we use a fan out of B instead of B, following ideas from [5, 10]. The external interval tree on a set of intervals I with endpoints in a xed set E of size N is de ned as follows. We assume without loss of generality that the endpoints of the intervals in I are distinct and that jEj = B for some i 0) The base tree T is a perfectly balanced ....

L. Arge, D. E. Vengro, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295-310, 1995. To appear in special issues of Algorithmica on Geographical Information Systems.

.... be designed using the distributionsweeping technique [86] Several other data structures can be constructed efficiently using buffers, and the buffer tree technique has been used to develop several other data structures which in turn have been used to develop algorithms in many different areas [25, 29, 20, 21, 107, 15, 76, 46, 144, 145, 96, 44, 136]. Priority queues. External buffered priority queues have been extensively researched because of their applications in graph algorithms. Arge showed how to perform deletemin operations on a basic buffer tree in amortized O( 1 B log M=B N B ) I Os [14] Note that in this case the deletemin ....

....can be stored about each multislab in O(1) blocks. Similar ideas have been utilized in several other external data structures [14, 25, 3, 28] Variants of the external interval tree structure, as well as applications of it in isosurface extraction, have been considered by Chiang and Silva [29, 60, 62, 61] (see also [7] Planar point location. The planar point location problem is defined as follows: Given a planar subdivision with N vertices (i.e. a decomposition of the plane into polygonal regions induced by a straight line planar graph) construct a data structure so that the face containing a ....

[Article contains additional citation context not shown here]

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295--310, 1995. To appear in special issues of Algorithmica on Geographical Information Systems.

.... External Memory (co authored with Vitter) OBDD] The I O Complexity of Ordered Binary Decision Diagram Manipulation [LowB] A General Lower Bound on the I O Complexity of Comparison based Algorithms (co authored with Knudsen and Larsen) Extended abstract versions of the papers have appeared in [11, 15, 16, 12, 13]. In the survey we refer to the papers as indicated above. The survey part of the thesis is divided into four chapters. In Chapter 2 we discuss basic paradigms for designing I O efficient algorithms and I O complexity of fundamental problems. This leads to a survey of external memory results in ....

....papers also deal with fundamental problems such as permutation, sorting and matrix transposition. The problem of implementing various classes of permutations has been addressed in [47, 48, 50] More recently researchers have moved on to more specialized problems in the computational geometry [11, 15, 34, 40, 67, 74, 79, 110, 121, 130, 137], graph [12, 40, 42, 97] and string areas [44, 56, 57] As already mentioned the number of I O operations needed to read the entire input is N=B and for convenience we call this quotient n. We use the term scanning to describe the fundamental primitive of reading (or writing) all elements in a ....

[Article contains additional citation context not shown here]

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, LNCS 979, pages 295--310, 1995. A full version is to appear in special issue of Algorithmica.

....Computation In recent years, I O efficient algorithms for a wide variety of problems have been developed. These include algorithms from the domains of sorting [AV88, Arg94, NV90, NV93, VS94] permuting [CSW94, Cor93, Cor92] computational geometry [GTVV93] line segment intersection [AVV95] graph algorithms [CGG 95] and scientific computation [VV95] The TPIE library [Ven95, Ven94] supports efficient implementation of many of these algorithms. A common theme in many of these algorithms is that they make a series of passes through their data; each pass reads most or all of ....

Lars Arge, Darren Erik Vengroff, and Jeffrey Scott Vitter. External-memory algorithms for processing line segments in georgraphic information systems. In Proc. 3rd Europ. Symp. on Algorithms, LNCS, Corfu, Greece, September 1995. Springer-Verlag. To appear.

....coming in from multiple processors. 1. 1 Summary of this Paper We present a new algorithm for the filter step called Scalable Sweeping Based Spatial Join (SSSJ) The algorithm uses several techniques for I O efficient computing recently proposed in computational geometry [APR 98, GTVV93, Arg95, AVV98, Arg97] plus the well known internal memory plane sweeping technique (see, e.g. PS85] It achieves theoretically optimal worst case bounds on both internal computation time and I O transfers, while also being efficient on the more wellbehaved data sets common in practice. We present ....

....be used as a building block in the SSSJ algorithm described in the next section. We point out that this section is based on the results and theoretical framework developed in [APR 98] The algorithm uses the distribution sweeping technique developed in [GTVV93] and further developed in [Arg95, AVV98] Following Aggarwal and Vitter [AV88] we use the following I O model: We make the assumption that each access to disk transmits one disk block with units of data, and we count this as one I O operation. We denote the total amount of main memory by . We assume that we are given two sets and In ....

L. Arge, D. E. Vengroff, and J. S. Vitter. Externalmemory algorithms for processing line segments in geographic information systems. Algorithmica (to appear in special issues on Geographical Information Systems), 1998. Extended abstract appears in Proc. of Third European Symposium on Algorithms, ESA'95.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. European Symp. Algorithms, LNCS 979, pages 295--310, 1995.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, pages 295--310. LNCS 979, Springer-Verlag, Berlin, 1995. A complete version (to appear in a special issue of Algorithmica) appears as BRICS Technical Report RS-96-12, University of Aarhus.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, pages 295--310. LNCS 979, Springer-Verlag, Berlin, 1995. A complete version (to appear in a special issue of Algorithmica) appears as BRICS Technical Report RS-96-12, University of Aarhus.

No context found.

L. Arge, D. E. Vengro#, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annu. European Sympos. Algorithms, LNCS 979, 295--310, 1995.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, pages 295--310. LNCS 979, Springer-Verlag, Berlin, 1995. A complete version (to appear in a special issue of Algorithmica) appears as BRICS Technical Report RS-96-12, University of Aarhus.

No context found.

L. Arge, D. Vengroff, and J. S. Vitter. External-Memory Algorithms for Processing Line Segments in Geographic Information Systems. In Proc. of the 3rd Annual European Symp. on Algorithms, pages 295--310, 1995.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, pages 295-- 310. LNCS 979. Springer-Verlag, Berlin, 1995. A complete version (to appear in special issue of Algorithmica) appears as BRICS Technical Report RS-96-12, University of Aarhus.

No context found.

L. Arge, D. E. Vengroff, and J. S. Vitter. External-memory algorithms for processing line segments in geographic information systems. In Proc. Annual European Symposium on Algorithms, pages 295--310. LNCS 979, Springer-Verlag, Berlin, 1995. A complete version (to appear in a special issue of Algorithmica) appears as BRICS Technical Report RS-96-12, University of Aarhus.

No context found.

Lars Arge, Darren Erik Vengrooe, and Jeoerey Scott Vitter. Externalmemory algorithms for processing line segments in geographic information systems. Algorithmica, 1998.

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