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86
Two simplified algorithms for maintaining order in a list
 PROCEEDINGS OF THE 10TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2002
"... In the OrderMaintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, ..."
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Cited by 61 (9 self)
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In the OrderMaintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.
Online data structures in external memory
 Proc. Annual International Colloquium on Automata, Languages, and Programming, LNCS 1644
, 1999
"... The data sets for many of today's computer applications are too large to fit within the computer's internal memory and must instead be stored on external storage devices such as disks. A major performance bottleneck can be the input/output communication (or I/O) between the external and in ..."
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Cited by 59 (6 self)
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The data sets for many of today's computer applications are too large to fit within the computer's internal memory and must instead be stored on external storage devices such as disks. A major performance bottleneck can be the input/output communication (or I/O) between the external and internal memories. In this paper we discuss a variety of online data structures for external memory, some very old and some very new, such as hashing (for dictionaries), Btrees (for dictionaries and 1D range search), buffer trees (for batched dynamic problems), interval trees with weightbalanced Btrees (for stabbing queries), priority search trees (for 3sided 2D range search), and Rtrees and other spatial structures. We also discuss several open problems along the way.
Efficient Searching with Linear Constraints (Extended Abstract)
"... ) Pankaj K. Agarwal Lars Arge y Jeff Erickson z Paolo G. Franciosa x Jeffrey Scott Vitter  Abstract We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear c ..."
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Cited by 56 (17 self)
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) Pankaj K. Agarwal Lars Arge y Jeff Erickson z Paolo G. Franciosa x Jeffrey Scott Vitter  Abstract We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d = 2, we present the first nearlinear size data structures that can answer linearconstraint queries using an optimal number of I/Os. We also present a linearsize data structure that can answer queries efficiently in the worst case. We combine these two approaches to obtain tradeoffs between space and query time. Finally, we show that some of our techniques extend to higher dimensions d. Center for Geometric Computing, Computer...
Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
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Cited by 38 (12 self)
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In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms
Managing Intervals Efficiently in ObjectRelational Databases
 IN PROC. OF THE 26TH INT’L CONFERENCE ON VERY LARGE DATABASES (VLDB
, 2000
"... Modern database applications show a growing demand for efficient and dynamic management of intervals, particularly for temporal and spatial data or for constraint handling. Common approaches require the augmentation of index structures which, however, is not supported by existing relational da ..."
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Cited by 35 (2 self)
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Modern database applications show a growing demand for efficient and dynamic management of intervals, particularly for temporal and spatial data or for constraint handling. Common approaches require the augmentation of index structures which, however, is not supported by existing relational database systems. By design, the new Relational Interval Tree (RItree) employs builtin indexes on an astheyare basis and is easy to implement. Whereas
Optimal External Memory Interval Management
, 2002
"... In this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be used in an optimal solution to the dynamic interval management problem, which is a central pro ..."
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Cited by 31 (6 self)
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In this paper we present the external interval tree, an optimal external memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The external interval tree can be used in an optimal solution to the dynamic interval management problem, which is a central problem for objectoriented and temporal databases and for constraint logic programming. Part of the structure uses a novel weightbalancing technique for efficient worstcase manipulation of balanced trees of independent interest. The external interval tree, as well at our new balancing technique, have recently been used to develop several efficient external data structures.
I/OEfficient Dynamic Planar Point Location
"... We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions and de ..."
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Cited by 29 (17 self)
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We present the first provably I/Oefficient dynamic data structure for point location in a general planar subdivision. Our structure uses O(N/B) disk blocks to store a subdivision of size N , where B is the disk block size. Queries can be answered in ... I/Os in the worstcase, and insertions and deletions can be performed in ... and ... I/Os amortized, respectively. Previously, an I/Oefficient dynamic point location structure was only known for monotone subdivisions. Part of our data structure...
ExternalMemory Algorithms with Applications in Geographic Information Systems
 Algorithmic Foundations of GIS
, 1997
"... In the design of algorithms for largescale applications it is essential to consider the problem of minimizing Input/Output (I/O) communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this n ..."
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Cited by 26 (9 self)
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In the design of algorithms for largescale applications it is essential to consider the problem of minimizing Input/Output (I/O) communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this note we survey the recent developments in externalmemory algorithms with applications in GIS. First we discuss the AggarwalVitter I/Omodel and illustrate why normal internalmemory algorithms for even very simple problems can perform terribly in an I/Oenvironment. Then we describe the fundamental paradigms for designing I/Oefficient algorithms by using them to design efficient sorting algorithms. We then go on and survey externalmemory algorithms for computational geometry problems  with special emphasis on problems with applications in GIS  and techniques for designing such algorithms: Using the orthogonal line segment intersection problem we illustrate the distributionsweeping and ...
A Framework for Index Bulk Loading and Dynamization
, 2001
"... In this paper we investigate automated methods for externalizing internal memory data structures. We consider a class of balanced trees that we call weightbalanced partitioning trees (or wptrees) for indexing a set of points in R d . Wellknown examples of wptrees include kd trees, BBDtre ..."
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Cited by 22 (14 self)
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In this paper we investigate automated methods for externalizing internal memory data structures. We consider a class of balanced trees that we call weightbalanced partitioning trees (or wptrees) for indexing a set of points in R d . Wellknown examples of wptrees include kd trees, BBDtrees, pseudoquadtrees, and BARtrees. Given an efficient external wptree construction algorithm, we present a general framework for automatically obtaining a dynamic external data structure. Using this framework together with a new general construction (bulk loading) technique of independent interest, we obtain data structures with guaranteed good update performance in terms of I/O transfers. Our approach gives considerably improved construction and update I/O bounds for e.g. external kdtrees and BBDtrees.
I/Oefficient algorithms for contourline extraction and planar graph blocking (Extended Abstract)
 IN PROCEEDINGS OF THE 10TH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1998
"... For a polyhedral terrain \Sigma, the contour at zcoordinate h, denoted Ch , is defined to be the intersection of the plane z = h with \Sigma. In this paper, we study the contourline extraction problem, where we want to preprocess \Sigma into a data structure so that given a query zcoordinate h, ..."
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Cited by 19 (1 self)
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For a polyhedral terrain \Sigma, the contour at zcoordinate h, denoted Ch , is defined to be the intersection of the plane z = h with \Sigma. In this paper, we study the contourline extraction problem, where we want to preprocess \Sigma into a data structure so that given a query zcoordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINs). We present an I/Ooptimal algorithm for this problem which stores a terrain \Sigma with N vertices using O(N=B) blocks, where B is the size of a disk block, so that for any query h, the contour Ch can be computed using O(log B N + jCh j=B) I/O operations, where jCh j denotes the size of Ch .