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97
ExternalMemory Graph Algorithms
, 1995
"... We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for der ..."
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Cited by 175 (24 self)
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We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for deriving externalmemory lower bounds via reductions from a problem we call the "proximate neighbors" problem. We use this technique to derive nontrivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. ffl PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not workoptimal. We apply this to derive a number of optimal (and simple) externalmemory graph algorithms. ffl Timeforward processing. We present a general technique for evaluating circuits (or "circuitlike" computations) in external memory. We also use this in a deterministic list rank...
Indexing moving points
, 2003
"... We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an in ..."
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Cited by 168 (13 self)
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We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t; report all K points of S that lie inside R at time t: We first present an indexing structure that, for any given constant e> 0; uses OðN=BÞ disk blocks and answers a query in OððN=BÞ 1=2þe þ K=BÞ I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can be changed, in Oðlog 2 B NÞ I/Os. Next, we present a general approach that improves the query time if the queries arrive in chronological order, by allowing the index to evolve over time. We obtain a tradeoff between the query time and the number of times the index needs to be updated as the points move. We also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate
The String BTree: A New Data Structure for String Search in External Memory and its Applications.
 Journal of the ACM
, 1998
"... We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by a ..."
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Cited by 122 (12 self)
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We introduce a new textindexing data structure, the String BTree, that can be seen as a link between some traditional externalmemory and stringmatching data structures. In a short phrase, it is a combination of Btrees and Patricia tries for internalnode indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String BTree overcomes the theoretical limitations of inverted files, Btrees, prefix Btrees, suffix arrays, compacted tries and suffix trees. String Btrees have the same worstcase performance as Btrees but they manage unboundedlength strings and perform much more powerful search operations such as the ones supported by suffix trees. String Btrees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication.
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 113 (20 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
Terrain Simplification Simplified: A General Framework for ViewDependent OutofCore Visualization
, 2002
"... This paper describes a general framework for outofcore rendering and management of massive terrain surfaces. The two key components of this framework are: viewdependent refinement of the terrain mesh; and a simple scheme for organizing the terrain data to improve coherence and reduce the number o ..."
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Cited by 81 (2 self)
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This paper describes a general framework for outofcore rendering and management of massive terrain surfaces. The two key components of this framework are: viewdependent refinement of the terrain mesh; and a simple scheme for organizing the terrain data to improve coherence and reduce the number of paging events from external storage to main memory. Similar to several previously proposed methods for viewdependent refinement, we recursively subdivide a triangle mesh defined over regularly gridded data using longestedge bisection. As part of this single, perframe refinement pass, we perform triangle stripping, view frustum culling, and smooth blending of geometry using geomorphing. Meanwhile, our refinement framework supports a large class of error metrics, is highly competitive in terms of rendering performance, and is surprisingly simple to implement. Independent
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 81 (36 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
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 76 (30 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.
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 75 (15 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...
Improved Algorithms and Data Structures for Solving Graph Problems in External Memory
 In Proc. IEEE Symp. on Parallel and Distributed Processing
, 1996
"... Recently, the study of I/Oefficient algorithms has moved beyond fundamental problems of sorting and permuting and into wider areas such as computational geometry and graph algorithms. With this expansion has come a need for new algorithmic techniques and data structures. In this paper, we present I ..."
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Cited by 75 (0 self)
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Recently, the study of I/Oefficient algorithms has moved beyond fundamental problems of sorting and permuting and into wider areas such as computational geometry and graph algorithms. With this expansion has come a need for new algorithmic techniques and data structures. In this paper, we present I/Oefficient analogues of wellknown data structures that we show to be useful for obtaining simpler and improved algorithms for several graph problems. Our results include improved algorithms for minimum spanning trees, breadthfirst search, and singlesource shortest paths. The descriptions of these algorithms are greatly simplified by their use of welldefined I/Oefficient data structures with good amortized performance bounds. We expect that I/Oefficient data structures such as these will be a useful tool for the design of I/Oefficient algorithms. 1. Introduction 1.1. Background and model The study of I/Oefficient algorithms has been receiving increased attention as increases in pro...