L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....we require: 1. an efficient view dependent multiresolution triangulation and rendering framework that can be dynamically modified, and 2. support for rendering from external memory which includes paging of view dependent LOD mesh data from disk. External memory algorithms and data structures [1, 2] present a unique set of challenges not encountered in traditional mainmemory techniques. Some efforts have been made in scientific visualization to develop external memory algorithms (see abstract Figure 1: A model of Michaelangelo s David statue, comprising over 8.25 million polygons. The model ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, Department of Computer Science, University of Aarhus (Denmark), 1996.

....versa external R heaps:del min 31 500 1000 1500 2000 2500 3000 0 2e 07 4e 07 6e 07 8e 07 1e 08 1.2e 08 1.4e 08 Number of integers: Rheaps for sorting integers merg sort rheap sort(C=1000) Figure 4.9: Radix heaps for sorting integers 32 4. 2 Buffer Trees as Priority Queues Buffer trees [Arg96a] are lazy search trees, based on internal (a,b) trees. Using a fanout of M=B per node together with buffering of data, it is possible to achieve an amortized I O bound of O(1=B log M=B n=B) per operation. In the absence of online changes this is optimal [Arg96a] As buffer trees are general ....

....as Priority Queues Buffer trees [Arg96a] are lazy search trees, based on internal (a,b) trees. Using a fanout of M=B per node together with buffering of data, it is possible to achieve an amortized I O bound of O(1=B log M=B n=B) per operation. In the absence of online changes this is optimal [Arg96a] As buffer trees are general search trees they can be used for a variety of problems like sorting, priority queues, etc. For example if they are used in a tree sort algorithm, this immediately leads to an I O optimal sorting algorithm. Unfortunately, the data structure is quite complicated. We ....

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L. Arge. Efficient external-memory data structures and applications. PhD thesis, University of Aarhus, 1996.

....(in an amortized sense) memory adaptive buffer tree. This result is particularly significant with respect to the extendibility of our techniques to diverse applications since the buffer tree is an I O optimal data structure for several several applications involving batched dynamic problems [Arg96, Vit98] including such time consuming operations as bulk loading of B trees and R trees [AHVV98] In Section 13, we present simple techniques resulting in a dynamically optimal algorithm for memory adaptive matrix multiplication and LU factorization; our techniques can thus form a basis for ....

.... buffer tree wrapper , resulting in I O optimal (in an amortized sense [Arg94] algorithms for several applications consisting of batched dynamic problems. These include improved graph algorithms, ordered binary decision disgrams, external heaps and string sorting, among other applications. See [Arg96] and [Vit98] for details. More recent applications for the buffer tree include bulk loading operations on R trees and B trees [AHVV98] In order to present a concise description of our memory adaptive buffer tree, it is convenient to informally differentiate between two types of external ....

Lars Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, Department of Computer Science, University of Aarhus, 1996.

....I Os, respectively. For the special case of grid graphs the connected component and minimum spanning tree algorithms of [17] use O(sort(N) I Os. For the other three problems the best known algorithms, even for grid graphs, all N) I Os. See recent surveys for a complete reference on the field [12, 35]. 1.3 Our results In the first part of this paper (Sections 2 and 3) we develop I O efficient algorithms for several standard graph theoretic problems on grid graphs, and thus for many common GIS problems on gridbased terrains, as well as for the problem of computing flow accumulation on a ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....are performed in parallel. If D log D n=r, the n=r adjacency lists to be considered in a phase will distribute almost evenly over the disks whp, and hence the time spent in reading adjacency lists is O(n=D m= DB) whp. We use a priority queue without decreaseKey operation (e.g. buffer trees [2]) and insert a node as often as it has incoming edges (each edge may give a different tentative distance) When a node is removed for the first time its bit is set. Later values for that node are ignored. The total I O complexity for this approach is given by O( B ) I Os whp. The number of ....

L. Arge. Efficient external-memory data structures and applications. PhD thesis, University of Aarhus, BRICS-DS-96-3, 1996.

....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 ....

Arge, L. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....B ) I Os for every Bth Insert and every Bth DeleteMin operation in the worst case. The above structures assume that the internal memory can only fit O(B) elements, i.e. a constant number of blocks. Even faster solutions are possible if the whole capacity of the internal memory is utilized. Arge [5, 6] introduced an (a,b) tree structure that can be used to carry out any sequence of S Insert and DeleteMin operations with O( S B log M=B S M ) I Os. Fadel et al. 13] gave a heap structure with a similar I O performance but their bound depends on the size profile, not on S. Their heap structure ....

L. Arge. Efficient external-memory data structures and applications. BRICS Dissertation DS-96-3, Department of Computer Science, University of Aarhus, Arhus, 1996.

....algorithms developed using the methods presented in this thesis. Motivated by the goal of constructing I O efficient versions of commonly used in 2 M is the total size of the internal memories and P 0 is the number of processors CHAPTER 1. INTRODUCTION 11 ternal memory data structures, Arge [8, 9] proposed the data structuring paradigm, and in particular the buffer tree. A buffer tree is an external memory search tree, based on the (a; b) tree [62] which is a generalization of the B tree [27] It allows several update operations, such as insert, delete, search, deletemin, and it ....

....[27] It allows several update operations, such as insert, delete, search, deletemin, and it enables the transformation of a class of internal memory algorithms to external memory algorithms by exchanging the data structures used. A large number of external memory algorithms have been proposed [8, 9] using the buffer tree data structure, including sorting, priority queues, range trees, segment trees, and time forward processing. These in turn are subroutines for many external memory graph algorithms, such as expression tree evaluation, centroid decomposition, least common ancestor, minimum ....

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L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....they showed that sorting N items in external memory requires Theta( N B log M=B N B )I Os. Subsequently, I O efficient algorithms have been developed for several problem domains, including computational geometry, graph theory, and string processing. Refer to recent surveys for references [3, 4, 32]. The practical merits of the developed algorithms have been explored byanumber of authors [11, 31, 6, 5] 1 For simplicitywe concentrate on the two first measures in this paper. It can be shown that the asymptotic internal memory computation time of our new R tree algorithms is the same as for ....

....can be performed in O(log B N B ) I Os, since only nodes on a single root to leaf path are visited by the (routing as well as the rebalancing) algorithm. Our technique for efficiently performing bulk operations on R trees is a variant of the general buffer treetechnique introduced by Arge [2, 3]. Here wemodify the general technique in a novel way, since a straightforward application of the technique would result in an R tree with an (impractically large) fan out of M=B [28] The main idea is the following: We attach buffers to all R tree nodes on every blog B M 4B cth level of the ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....[2] considered sorting and related problems in the I O model and proved that sorting requires O( N=B) log M=B (N=B) O( N=B) log B N ) I Os. Subsequently, I O efficient algorithms and data structures have been developed for numerous problems see recent surveys for a sample of these results [3,4, 28]. Most previous results on point location in external memory have been either static or batched dynamic: Goodrich 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 ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, Universityof Aarhus, February/August 1996.

....which are provably optimal according to some stated model. Sorting, permutation and related problems in EM have been extensively studied [1, 11, 32, 26] I O optimal approaches to many computational geometry problems [21] and graph problems [10] have also been described. Data structures [3] and a number of applications [4] have been examined in this context. Some implementation work has also been done [29, 9, 13, 22] including some parallel processing EM implementations [14] Blocking of graphs for external memory searching was studied in [25] A recent survey appears in [30] The ....

Arge, L. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....requires Omega Gamma N log N) comparisions in the comparision model, requires Omega Gamma N B log M B N B ) I Os in the PDM model. EM algorithms have been proposed for a num 1 log M B N B is defined to mean maxf1; log M B N B g. ber of problems arising in computational geometry [8, 6, 23, 32], geographical information systems [8, 43] and graphs [5, 15, 34, 41] Over the last few years, comprehensive computing and cost models, that incorporate multi disks and multi processors have been proposed [17, 25, 28, 35] Several suggestions have been made regarding the simulation of parallel ....

Arge, L. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....For the special case of grid graphs the connected component and minimum spanning tree algorithms of [17] use O(sort(N) I Os. For the other three problems the best known algorithms, even for grid graphs, all use Omega Gamma N) I Os. See recent surveys for a complete reference on the field [12, 35]. 1.3 Our results In the first part of this paper (Sections 2 and 3) we develop I O efficient algorithms for several standard graph theoretic problems on grid graphs, and thus for many common GIS problems on gridbased terrains, as well as for the problem of computing flow accumulation on a ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....for bulk loading R trees that actually make use of dynamic insertion rules [8, 13] These methods are in general applicable to balanced tree structures which resemble B trees, including a large class of multidimensional index structures. Both techniques are based on the notion of the buffer tree [7], wherein each internal node of the tree structure contains a buffer of records. The buffers enable effective use of available main memory, and result in large savings in I O cost over the regular dynamic insertion method (but generally in at least as much CPU cost) In the method proposed by van ....

L. Arge. Efficient external-memory data structures and applications. BRICS dissertation series, DS-96-3, University of Aarhus, 1996.

....nodes fill up main memory almost totally. More formally, we assume that and C m hold. According to [BSW 97] the creation of the index is based on the idea of associating an external buffer with each of the index nodes. Arge has originally proposed this technique for the so called buffer tree [Arg 96] In order to create the index in bulk, the buffers are used for processing multiple insertions of data records in the target index structure simultaneously. An insertion process is in one of the three states active, blocked or terminated. Only one of the insertion processes is active at a time, ....

L. Arge, "Efficient External-Memory Data Structures and Applications", BRICS Dissertation Series, DS-96-3, University of Aarhus, 1996.

....are performed in parallel. If D log D n=r, the n=r adjacency lists to be considered in a phase will distribute almost evenly over the disks whp, and hence the time spent in reading adjacency lists is O(n=D m= DB) whp. We use a priority queue without decreaseKey operation (e.g. buffer trees [2]) and insert a node as often as it has incoming edges (each edge may give a different tentative distance) When a node is removed for the first time its bit is set. Later values for that node are ignored. The total I O complexity for this approach is given by O( n D m DB log S=B m B ) I Os ....

L. Arge. Efficient external-memory data structures and applications. PhD thesis, University of Aarhus, BRICS-DS-96-3, 1996.

.... The theoretical framework of the algorithms in this paper is based on the Parallel Disk I O Model (PDM) proposed by Vitter and Shriver [28] Permutations and sorting have been very widely studied in the context of this model, see [2, 1, 9, 20, 27] Algorithms for problems in computational geometry [15, 4, 3, 8, 23], graph theory [7, 19, 3] and GIS [4] have been presented. A number of general paradigms for designing external memory algorithms have been proposed. These include simulation [7, 12, 15, 22] merging [5, 20] distribution [21, 15, 7] and data structuring [2] Recently there has been an ....

.... algorithms in this paper is based on the Parallel Disk I O Model (PDM) proposed by Vitter and Shriver [28] Permutations and sorting have been very widely studied in the context of this model, see [2, 1, 9, 20, 27] Algorithms for problems in computational geometry [15, 4, 3, 8, 23] graph theory [7, 19, 3], and GIS [4] have been presented. A number of general paradigms for designing external memory algorithms have been proposed. These include simulation [7, 12, 15, 22] merging [5, 20] distribution [21, 15, 7] and data structuring [2] Recently there has been an increasing interest in ....

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L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, 1996.

....new list I 0 = x 1 ; x N ) such that x i = x j ; i j = x i = x i 1 ; i.e. all records with equal keys appear contiguously in I 0 . Grouping differs from sorting in that the order among elements of different keys is arbitrary. It also differs from duplicate elimination [5,17], in that the latter returns only a list of distinct keys in I. Grouping solves duplicate elimination, however, using one additional scan to identify the distinct keys. We first assume that the keys of the elements of I are integers in the range [1; K] we can scan I once to find K, if necessary. ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, Dept. of Computer Science, University of Aarhus, Denmark, 1996.

....O(log 2 N B ) I Os for every Bth Insert and every Bth DeleteMin operation. The above structures assume that the internal memory can only fit O(B) elements, i.e. a constant number of blocks. Even faster solutions are possible if the whole capacity of the internal memory is utilized. Arge [5, 6] introduced an (a,b) tree structure that can be used to carry out any sequence of S Insert and DeleteMin operations with O( S B log M=B S M ) I Os. Fadel et al. 13] gave a heap structure with a similar I O performance but their bound depends on the size profile, not on S. Their heap structure ....

L. Arge. Efficient external-memory data structures and applications. BRICS Dissertation DS96 -3, Department of Computer Science, University of Aarhus, Arhus, 1996.

....disks for a large range of integers r. 1.2 Previous Work Sorting, permutation and related problems in EM have been extensively studied [1, 12, 27, 26, 20] I O optimal approaches to many computational geometry problems [17] and graph problems [11] have also been described. Data structures [3, 5, 22] and a number of applications [4] have been examined in this context. Some implementation work has also been done [24, 25, 10] A recent survey is included in [5] The classical EM model is described in [1] More complex models have been proposed as well, incorporating a hierarchy of memory layers ....

....approaches to many computational geometry problems [17] and graph problems [11] have also been described. Data structures [3, 5, 22] and a number of applications [4] have been examined in this context. Some implementation work has also been done [24, 25, 10] A recent survey is included in [5]. The classical EM model is described in [1] More complex models have been proposed as well, incorporating a hierarchy of memory layers rather than the two level memory model of [1] One such model is described in [2] and sorting for this model is studied in [26] Such models are interesting ....

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L. Arge. Efficient External-Memory Data Structures and Applications, Ph.D Thesis, BRICS, University of Aarhus, 1996.

....to store segments in secondary structures such that queries can be answered efficiently. The starting idea behind our successful externalization of the structure, as compared with previous attempts [9, 35] is that the nodes in our structure have fan out p B instead of B, following ideas from [2, 3, 4]. The implications of this smaller fan out are explained later in this section. The external memory interval tree on a set of intervals I with endpoints in a fixed set E is defined in the following way (we assume without loss of generality that no two intervals in I have the same endpoint, and ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....search tree can be used in the context of insertion sort to sort optimally. If we use the standard external memory search tree, the B tree [12, 19] we get an O(N log B N) I O insertion sort. This algorithm s I O efficiency is a multiplicative factor of B log B (M=B) larger than optimal. In [6, 8] a so called buffer technique for lazy updates in external data structures is developed, and using this technique the buffer tree is designed. Using this structure in the external insertion sort yields an optimal sorting algorithm. As far as the general string sorting problem is concerned, there ....

....introduction the algorithm for short strings is obtained by applying either this long string algorithm or the short string algorithm for Model A. Our solution for long strings will be based upon the SB tree and the buffer tree data structures which we briefly review below (we refer the reader to [6, 8, 20] for more details) We then describe our improved algorithm which is a combination of these two data structures. The Buffer Tree. The basic buffer tree on R integer keys is a B tree (or rather an (a; b) tree [31] with fanout Theta(M=B) and with blocks of elements in the leaves; thus the tree ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February /August 1996.

....[2] considered sorting and related problems in the I O model and proved that sorting requires O( N=B) log M=B (N=B) O( N=B) log B N) I Os. Subsequently, I O efficient algorithms and data structures have been developed for numerous problems see recent surveys for a sample of these results [3, 4, 28]. Most previous results on point location in external memory have been either static or batched dynamic: Goodrich 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 ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

.... sorting and permuting [1, 38] computational geometry [2, 7, 22] string algorithms [6, 19] and graph algorithms [3, 11, 21, 27, 34] There has recently been growing interest in developing I O efficient geometric algorithms with applications in GIS [5, 7, 22] see also the recent survey by Arge [4]. There has also been a lot of work in the database community on I O algorithms for GIS applications [14, 26, 10, 24, 30, 32, 29] For the contour line extraction problem, van Kreveld (see also the recent work of van Kreveld et al. 37] gives an internal memory algorithm for preprocessing a ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....is applied to a contour before it is displayed. 1. 3 Previous results In the last few years, considerable attention has been given to the development of I O efficient algorithms in many problem domains, including sorting, graph algorithms, string algorithms, computational geometry, and GIS; see [1, 2, 3, 4, 5, 8, 19, 21, 27] and the references therein. Although the contour line extraction problem has been well studied for terrains stored as raster images (for example, see the Marching Cubes algorithm [18] not much work has been done when terrains are stored as TINs. van Kreveld [23] gives an internal memory ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, Denmark, February/August 1996.

....log m n) I Os. 1 I O efficient algorithms were later developed for several other problem domains, including computational geometry [1, 3, 6, 18] string problems [5] and graph theory [3, 12, 37, 25] See the mentioned papers for more complete references; a recent survey is also included in [4]. In the database literature a lot of attention has also been given to I O efficient computation, but with more emphasis on practical performance on real life data. Special attention has been given to the development of I O efficient spatial join algorithms [10, 20, 21, 24, 26, 27, 30] A number ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

.... authors have considered the difficult problem of sorting optimally on parallel disks [5, 21, 73, 71] The problem of implementing various classes of permutations has been addressed in [38, 39, 41] More recently researchers have moved on to more specialized problems in the computational geometry [12, 14, 19, 32, 53, 99], graph theoretical [13, 14, 32, 34, 52, 66] and string processing areas [15, 35, 45, 46] 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. One normally uses the term scanning to describe the fundamental ....

.... of sorting optimally on parallel disks [5, 21, 73, 71] The problem of implementing various classes of permutations has been addressed in [38, 39, 41] More recently researchers have moved on to more specialized problems in the computational geometry [12, 14, 19, 32, 53, 99] graph theoretical [13, 14, 32, 34, 52, 66] and string processing areas [15, 35, 45, 46] 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. One normally uses 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. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

.... 5, 53, 31, 2, 11, 34, 44, 47, 12, 50, 17, 1] string processing [28, 29, 9] and graph theoretic computation [6, 24, 38, 35] Some encouraging experimental results regarding the practical merits of the developed algorithms have also been obtained [23, 51, 11, 33] Recent surveys can be found in [7, 8]. 1.3 Our Results In this paper, we combine and modify in novel ways several of the previously known techniques for designing efficient algorithms for external memory. In particular we use the distribution sweeping and batch filtering paradigms of [32] and the buffer tree data structure of [5] ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

....and Vitter [1] considered sorting and related problems in the I O model and proved that sorting requires Theta( N B log M=B N B ) I Os. Subsequently, I Oefficient algorithms and data structures have been developed for numerous problems see recent surveys for a sample of these results [2, 3, 26]. All previous results on point location in external memory have been either static or batched dynamic: Goodrich et al. 16] designed a static data structure using O(N=B) space to store a monotone subdivision of size N so that a query can be answered in optimal O(log B N) I Os. They also developed ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD Thesis, University of Aarhus, 1996.

....computation time of our new R tree algorithms is the same as for the traditional algorithms. I Os. Subsequently, I O efficient algorithms have been developed for several problem domains, including computational geometry, graph theory, and string processing. Refer to recent surveys for references [3, 4, 32]. The practical merits of the developed algorithms have been explored by a number of authors [11, 31, 6, 5] Much of this work uses the Transparent Parallel I O programming Environment (TPIE) 29, 30, 31] TPIE is a set of C functions and templated classes that allow for simple, efficient, and ....

....can be performed in O(log B N B ) I Os, since only nodes on a single root to leaf path are visited by the (routing as well as the rebalancing) algorithm. Our technique for efficiently performing bulk operations on R trees is a variant of the general buffer tree technique introduced by Arge [2, 3]. Here we modify the general technique in a novel way, since a straightforward application of the technique would result in an R tree with an (impractically large) fan out of m [28] The main idea is the following: We attach buffers to all R tree nodes on every blog B M 4B cth level of the tree; ....

L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.

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ARGE,L.Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.

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ARGE,L.Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.

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ARGE,L.Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.

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ARGE,L.Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. BRICS Dissertation Series, DS-963, University of Aarhus, 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. Ph.D. thesis, University of Aarhus, February/August 1996.

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L. Arge. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Arhus, 1996.

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ARGE, L. Efficient External-Memory Data Structures and Applications. PhD thesis, University of Aarhus, February/August 1996.

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