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I/Oefficient batched unionfind and its applications to terrain analysis
 IN PROC. 22ND ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2006
"... Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N union and find opera ..."
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Cited by 23 (9 self)
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Despite extensive study over the last four decades and numerous applications, no I/Oefficient algorithm is known for the unionfind problem. In this paper we present an I/Oefficient algorithm for the batched (offline) version of the unionfind problem. Given any sequence of N union and find operations, where each union operation joins two distinct sets, our algorithm uses O(SORT(N)) = O ( N B log M/B N I/Os, where M is the memory size and B is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses O(SORT(N) + MST(N)) I/Os, where MST(N) is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical O(SORT(N) log ( N M))I/O algorithm for this problem, which we have implemented. We are interested in the unionfind problem because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over R2, and many problems that deal with such functions require a unionfind data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/Oefficient algorithms are needed to process this data efficiently. In this paper, we study two terrainanalysis problems that benefit from a unionfind data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first O(SORT(N))I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with N vertices. Finally, we report some preliminary experimental results, showing that our algorithms give orderofmagnitude improvement over previous methods on large data sets that do not fit in memory.
TerraStream: From elevation data to watershed hierarchies
 PROC. ACM SYMPOS. ON ADVANCES IN GEOGRAPHIC INFORMATION SYSTEMS
"... We consider the problem of extracting a river network and a watershed hierarchy from a terrain given as a set of irregularly spaced points. We describe TerraStream, a “pipelined” solution that consists of four main stages: construction of a digital elevation model (DEM), hydrological conditioning, e ..."
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Cited by 20 (12 self)
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We consider the problem of extracting a river network and a watershed hierarchy from a terrain given as a set of irregularly spaced points. We describe TerraStream, a “pipelined” solution that consists of four main stages: construction of a digital elevation model (DEM), hydrological conditioning, extraction of river networks, and construction of a watershed hierarchy. Our approach has several advantages over existing methods. First, we design and implement the pipeline so each stage is scalable to massive data sets; a single nonscalable stage would create a bottleneck and limit overall scalability. Second, we develop the algorithms in a general framework so that they work for both TIN and grid DEMs. TerraStream is flexible and allows users to choose from various models and parameters, yet our pipeline is designed to reduce (or eliminate) the need for manual intervention between stages. We have implemented TerraStream and present experimental results on real elevation point sets that show that our approach handles massive multigigabyte terrain data sets. For example, we can process a data set containing over 300 million points—over 20GB of raw data—in under 26 hours, where most of the time (76%) is spent in the initial CPUintensive DEM construction stage.
I/OEfficient Construction of Constrained Delaunay Triangulations
"... In this paper, we designed and implemented an I/Oefficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( N B logM/B N B) I/Os for triangulating N points in the plane, where M ..."
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Cited by 19 (5 self)
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In this paper, we designed and implemented an I/Oefficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( N B logM/B N B) I/Os for triangulating N points in the plane, where M is the memory size and B is the disk block size. If there are more constraining segments, the theoretical bound does not hold, but in practice the performance of our algorithm degrades gracefully. Through an extensive set of experiments with both synthetic and real data, we show that our algorithm is significantly faster than existing implementations.
A Survey of Distributed Workflow Characteristics and Resource Requirements
"... Workflows have been used to model repeatable tasks or operations in a number of different industries including manufacturing and software. In recent years, workflows are increasingly used in distributed resources and web services environments through resource models such as grid and cloud computing. ..."
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Cited by 9 (2 self)
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Workflows have been used to model repeatable tasks or operations in a number of different industries including manufacturing and software. In recent years, workflows are increasingly used in distributed resources and web services environments through resource models such as grid and cloud computing. These workflows often have disparate requirements and constraints that need to be accounted for during workflow orchestration. In this paper, we present workflow examples from different domains including bioinformatics and biomedical, weather and ocean modeling, astronomy detailing their data and computational requirements. 1
Surface Compression using Overdetermined Laplacian Approximation
"... We describe a surface compression technique to lossily compress elevation datasets. Our approach first approximates the uncompressed terrain using an overdetermined system of linear equations based on the Laplacian partial differential equation. Then the approximation is refined with respect to the ..."
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Cited by 6 (1 self)
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We describe a surface compression technique to lossily compress elevation datasets. Our approach first approximates the uncompressed terrain using an overdetermined system of linear equations based on the Laplacian partial differential equation. Then the approximation is refined with respect to the uncompressed terrain using an error metric. These two steps work alternately until we find an approximation that is good enough. We then further compress the result to achieve a better overall compression ratio. We present experiments and measurements using different metrics and our method gives convincing results.
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"... This paper investigates what is essentially a callbyvalue version of PCF under a complexitytheoretically motivated type system. The programming formalism, ATR1, has its firstorder programs characterize the polytime computable functions, and its secondorder programs characterize the type2 basic ..."
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This paper investigates what is essentially a callbyvalue version of PCF under a complexitytheoretically motivated type system. The programming formalism, ATR1, has its firstorder programs characterize the polytime computable functions, and its secondorder programs characterize the type2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR1types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The sizerestricted part is motivated by Bellantoni and Cook’s and Leivant’s implicit characterizations of polytime. The timerestricting part is an affine version of Barber and Plotkin’s DILL. Two semantics are constructed for ATR1. The first is a pruning of the naïve denotational semantics for ATR1. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR1’s time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR1 recursions, the solutions of which yield secondorder polynomial time bounds. The timecomplexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.
I/OEfficient Construction of Constrained
"... Abstract. In this paper, we designed and implemented an I/Oefficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( NB logM/B NB) I/Os for triangulating N points in the plane, ..."
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Abstract. In this paper, we designed and implemented an I/Oefficient algorithm for constructing constrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( NB logM/B NB) I/Os for triangulating N points in the plane, where M is the memory size and B is the disk block size. If there are more constraining segments, the theoretical bound does not hold, but in practice the performance of our algorithm degrades gracefully. Through an extensive set of experiments with both synthetic and real data, we show that our algorithm is significantly faster than existing implementations. 1 Introduction With the emergence of new terrain mapping technologies such as Laser altimetry (LIDAR), one can acquire millions of georeferenced points within minutes to hours. Converting this data into a digital elevation model (DEM) of the underlying terrain in an efficient manner is a challenging important problem. The socalled triangulated irregular network (TIN) is a widely used DEM, in which aterrain is represented as a triangulated xymonotone surface. One of the popularmethods to generate a TIN from elevation dataa cloud of points in
I/OEfficient Construction of Constrained Delaunay Triangulations
"... Abstract In this paper, we designed and implemented an I/Oefficient algorithm for constructingconstrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( NB logM/B NB) I/Os for triangulating Npoints in the plane, wh ..."
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Abstract In this paper, we designed and implemented an I/Oefficient algorithm for constructingconstrained Delaunay triangulations. If the number of constraining segments is smaller than the memory size, our algorithm runs in expected O ( NB logM/B NB) I/Os for triangulating Npoints in the plane, where M is the memory size and B is the disk block size. If there are moreconstraining segments, the theoretical bound does not hold, but in practice the performance of