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59
An asymptotically optimal multiversion Btree
, 1996
"... In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying these multiversion data efficiently, external storage structures are an absolute necessity. We propose a multiversion Btree that supports insertions and deletions of data ite ..."
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Cited by 187 (9 self)
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In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying these multiversion data efficiently, external storage structures are an absolute necessity. We propose a multiversion Btree that supports insertions and deletions of data items at the current version and range queries and exact match queries for any version, current or past. Our multiversion Btree is asymptotically optimal in the sense that the time and space bounds are asymptotically the same as those of the (singleversion) Btree in the worst case. The technique we present for transforming a (singleversion) Btree into a multiversion Btree is quite general: it applies to a number of hierarchical external access structures with certain properties directly, and it can be modified for others.
Indexing for data models with constraints and classes
 Journal of Computer and System Sciences
, 1996
"... We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects a ..."
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Cited by 114 (19 self)
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We examine I Oefficient data structures that provide indexing support for new data models. The database languages of these models include concepts from constraint programming (e.g., relational tuples are generated to conjunctions of constraints) and from objectoriented programming (e.g., objects are organized in class hierarchies). Let n be the size of the database, c the number of classes, B the page size on secondary storage, and t the size of the output of a query: (1) Indexing by one attribute in many constraint data models is equivalent to external dynamic interval management, which is a special case of external dynamic twodimensional range searching. We present a semidynamic data structure for this problem that has worstcase space O(n B) pages, query I O time O(logB n+t B) and O(logB n+(logB n) 2 B) amortized insert I O time. Note that, for the static version of this problem, this is the first worstcase optimal solution. (2) Indexing by one attribute and by class name in an objectoriented model, where objects are organized
Optimal Dynamic Interval Management in External Memory (Extended Abstract)
 IN PROC. IEEE SYMP. ON FOUNDATIONS OF COMP. SCI
, 1996
"... We present a space and I/Ooptimal externalmemory data structure for answering stabbing queries on a set of dynamically maintained intervals. Our data structure settles an open problem in databases and I/O algorithms by providing the first optimal externalmemory solution to the dynamic interval m ..."
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Cited by 81 (20 self)
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We present a space and I/Ooptimal externalmemory data structure for answering stabbing queries on a set of dynamically maintained intervals. Our data structure settles an open problem in databases and I/O algorithms by providing the first optimal externalmemory solution to the dynamic interval management problem, which is a special case of 2dimensional range searching and a central problem for objectoriented and temporal databases and for constraint logic programming. Our data structure simultaneously uses optimal linear space (that is, O(N/B) blocks of disk space) and achieves the optimal O(log B N + T/B) I/O query bound and O(log B N ) I/O update bound, where B is the I/O block size and T the number of elements in the answer to a query. Our structure is also the first optimal external data structure for a 2dimensional range searching problem that has worstcase as opposed to amortized update bounds. Part of the data structure uses a novel balancing technique for efficient worstcase manipulation of balanced trees, which is of independent interest.
Scalable Parallel Computational Geometry for Coarse Grained Multicomputers
 International Journal on Computational Geometry
, 1994
"... We study scalable parallel computational geometry algorithms for the coarse grained multicomputer model: p processors solving a problem on n data items, were each processor has O( n p ) AE O(1) local memory and all processors are connected via some arbitrary interconnection network (e.g. mesh, hype ..."
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Cited by 76 (14 self)
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We study scalable parallel computational geometry algorithms for the coarse grained multicomputer model: p processors solving a problem on n data items, were each processor has O( n p ) AE O(1) local memory and all processors are connected via some arbitrary interconnection network (e.g. mesh, hypercube, fat tree). We present O( Tsequential p + T s (n; p)) time scalable parallel algorithms for several computational geometry problems. T s (n; p) refers to the time of a global sort operation. Our results are independent of the multicomputer's interconnection network. Their time complexities become optimal when Tsequential p dominates T s (n; p) or when T s (n; p) is optimal. This is the case for several standard architectures, including meshes and hypercubes, and a wide range of ratios n p that include many of the currently available machine configurations. Our methods also have some important practical advantages: For interprocessor communication, they use only a small fixed numb...
Scalable sweepingbased spatial join
 IN PROC. 24TH INT. CONF. VERY LARGE DATA BASES, VLDB
, 1998
"... In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable SweepingBased Spatial Join (SSSJ), that achieves both efficiency on reallife data and robustness against highly skewed and worstcase d ..."
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Cited by 69 (7 self)
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In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable SweepingBased Spatial Join (SSSJ), that achieves both efficiency on reallife data and robustness against highly skewed and worstcase data sets. The algorithm combines a method with theoretically optimal bounds on I/O transfers based on the recently proposed distributionsweeping technique with a highly optimized implementation of internalmemory planesweeping. We present experimental results based on an efficient implementation of the SSSJ algorithm, and compare it to the stateoftheart PartitionBased SpatialMerge (PBSM) algorithm of Pate1 and DeWitt.
ExternalMemory Algorithms for Processing Line Segments in Geographic Information Systems
, 2007
"... In the design of algorithms for largescale applications it is essential to consider the problem of minimizing 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 paper we develop ..."
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Cited by 67 (25 self)
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In the design of algorithms for largescale applications it is essential to consider the problem of minimizing 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 paper we develop efficient externalmemory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red–blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.
Survey of spatiotemporal databases
 GeoInformatica
, 1999
"... Spatiotemporal databases aim to support extensions to existing models of Spatial Information Systems (SIS) to include time in order to better describe our dynamic environment. Although interest into this area has increased in the past decade, a number of important issues remain to be investigated. ..."
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Cited by 62 (6 self)
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Spatiotemporal databases aim to support extensions to existing models of Spatial Information Systems (SIS) to include time in order to better describe our dynamic environment. Although interest into this area has increased in the past decade, a number of important issues remain to be investigated. With the advances made in temporal database research, we can expect a more unified approach towards aspatial temporal data in SIS and a wider discussion on spatiotemporal data models. This paper provides an overview of previous achievements within the field and highlights areas currently receiving or requiring further investigation.
Indexing Animated Objects Using Spatiotemporal Access Methods
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... AbstractÐWe present a new approach for indexing animated objects and efficiently answering queries about their position in time and space. In particular, we consider an animated movie as a spatiotemporal evolution. A movie is viewed as an ordered sequence of frames, where each frame is a 2D space oc ..."
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Cited by 54 (7 self)
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AbstractÐWe present a new approach for indexing animated objects and efficiently answering queries about their position in time and space. In particular, we consider an animated movie as a spatiotemporal evolution. A movie is viewed as an ordered sequence of frames, where each frame is a 2D space occupied by the objects that appear in that frame. The queries of interest are range queries of the form, ªfind the objects that appear in area S between frames fi and fjº as well as nearest neighbor queries such as, ªfind the q nearest objects to a given position A between frames fi and fj.º The straightforward approach to index such objects considers the frame sequence as another dimension and uses a 3D access method (such as, an RTree or its variants). This, however, assigns long ªlifetimeº intervals to objects that appear through many consecutive frames. Long intervals are difficult to cluster efficiently in a 3D index. Instead, we propose to reduce the problem to a partialpersistence problem. Namely, we use a 2D access method that is made partially persistent. We show that this approach leads to faster query performance while still using storage proportional to the total number of changes in the frame evolution. What differentiates this problem from traditional temporal indexing approaches is that objects are allowed to move and/or change their extent continuously between frames. We present novel methods to approximate such object evolutions. We formulate an optimization problem for which we provide an optimal solution for the case where objects move linearly. Finally, we present an extensive experimental study of the proposed methods. While we concentrate on animated movies, our approach is general and can be applied to other spatiotemporal applications as well. Index TermsÐAccess methods, spatiotemporal databases, animated objects, multimedia. 1
The Snapshot Index, an I/OOptimal Access Method for Timeslice Queries
 Information Systems, An International Journal
, 1995
"... Abstract We present an access method for timeslice queries that reconstructs a past state s(t) of a timeevolving collection of objects, in O(log,, n + Is(t)l/b) I/O ‘8, where Is(t)1 denotes the size of the collection at time t, n is the total number of changes in the collection’s evolution and b i ..."
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Cited by 53 (18 self)
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Abstract We present an access method for timeslice queries that reconstructs a past state s(t) of a timeevolving collection of objects, in O(log,, n + Is(t)l/b) I/O ‘8, where Is(t)1 denotes the size of the collection at time t, n is the total number of changes in the collection’s evolution and b is the size of an I/O transfer. Changes include the addition, deletion or attribute modification of objects; they are assumed to occur in increasing time order and always affect the most current state of the collection (thus our index supports transactiontime.) The space used is 0 n/b) while the update processing is constant per change, i.e., independent of n. This is the first I I Ooptimal access method for this problem using O(n/b) space and O(1) updating (in the expected amortized sense due to the use of hashing.) This performance is also achieved for interval intersection temporal queries. An advantage of our approach is that its performance can be tuned to match particular application needs (trading space for query time and vice versa). In addition, the Snapshot Index can naturally migrate data on a writeonce optical medium while maintaining the same performance bounds.
Cache oblivious distribution sweeping
 IN PROC. 29TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES, AND PROGRAMMING (ICALP), VOLUME 2380 OF LNCS
, 2002
"... We adapt the distribution sweeping method to the cache oblivious model. Distribution sweeping is the name used for a general approach for divideandconquer algorithms where the combination of solved subproblems can be viewed as a merging process of streams. We demonstrate by a series of algorithms ..."
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Cited by 42 (10 self)
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We adapt the distribution sweeping method to the cache oblivious model. Distribution sweeping is the name used for a general approach for divideandconquer algorithms where the combination of solved subproblems can be viewed as a merging process of streams. We demonstrate by a series of algorithms for specific problems the feasibility of the method in a cache oblivious setting. The problems all come from computational geometry, and are: orthogonal line segment intersection reporting, the all nearest neighbors problem, the 3D maxima problem, computing the measure of a set of axisparallel rectangles, computing the visibility of a set of line segments from a point, batched orthogonal range queries, and reporting pairwise intersections of axisparallel rectangles. Our basic building block is a simplified version of the cache oblivious sorting algorithm Funnelsort of Frigo et al., which is of independent interest.