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Flow Computation on Massive Grid Terrains
 GEOINFORMATICA
, 2001
"... ... In this paper we present efficient algorithms for flow routing on massive terrains, extending our previous work on flow accumulation on massive terrains. We have implemented these algorithms in the Terraflow system, which is the first comprehensive terrain flow software system designed and optim ..."
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Cited by 16 (9 self)
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... In this paper we present efficient algorithms for flow routing on massive terrains, extending our previous work on flow accumulation on massive terrains. We have implemented these algorithms in the Terraflow system, which is the first comprehensive terrain flow software system designed and optimized for massive data. We compare the performance of Terraflow with that of state of the art commercial and opensource GIS systems. On large terrains, Terraflow outperforms existing systems by a factor of 2 to 1000, and is capable of solving problems no system was previously able to solve.
Efficient flow computation on massive grid terrain datasets
 GeoInform
, 2003
"... As detailed terrain data becomes available, GIS terrain applications target larger geographic areas at finer resolutions. Processing the massive datasets involved in such applications presents significant challenges to GIS systems and demands algorithms that are optimized for both data movement and ..."
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Cited by 11 (0 self)
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As detailed terrain data becomes available, GIS terrain applications target larger geographic areas at finer resolutions. Processing the massive datasets involved in such applications presents significant challenges to GIS systems and demands algorithms that are optimized for both data movement and computation. In this paper we present efficient algorithms for flow routing on massive grid terrain datasets, extending our previous work on flow accumulation. Our algorithms are developed in the framework of external memory algorithms and use I/Otechniques to achieve efficiency. We have implemented the algorithms in the Terraflow system, which is the first comprehensive terrain flow software system designed and optimized for massive data. We compare the performance of Terraflow with that of stateoftheart commercial and opensource GIS systems. On large terrains, Terraflow outperforms existing systems by a factor of 2 to 1000, and is capable of solving problems no system was previously able to solve. 1.
An Optimal CacheOblivious Priority Queue and its Application to Graph Algorithms
 SIAM JOURNAL ON COMPUTING
, 2007
"... We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ amortized memory transfers, where $M$ and $B$ are the memory and block transfer sizes of any two consecutive levels of a multilevel ..."
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Cited by 9 (0 self)
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We develop an optimal cacheoblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ amortized memory transfers, where $M$ and $B$ are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cacheoblivious data structure, $M$ and $B$ are not used in the description of the structure. Our structure is as efficient as several previously developed external memory (cacheaware) priority queue data structures, which all rely crucially on knowledge about $M$ and $B$. Priority queues are a critical component in many of the best known external memory graph algorithms, and using our cacheoblivious priority queue we develop several cacheoblivious graph algorithms.
I/Oefficient hierarchical watershed decomposition of grid terrain models
 In Proc. 12th International Symposium on Spatial Data Handling
, 2006
"... Summary. Recent progress in remote sensing has made massive amounts of high resolution terrain data readily available. Often the data is distributed as regular grid terrain models where each grid cell is associated with a height. When terrain analysis applications process such massive terrain models ..."
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Cited by 8 (5 self)
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Summary. Recent progress in remote sensing has made massive amounts of high resolution terrain data readily available. Often the data is distributed as regular grid terrain models where each grid cell is associated with a height. When terrain analysis applications process such massive terrain models, data movement between main memory and slow disk (I/O), rather than CPU time, often becomes the performance bottleneck. Thus it is important to consider I/Oefficient algorithms for fundamental terrain problems. One such problem is the hierarchical decomposition of a grid terrain model into watersheds–regions where all water flows towards a single common outlet. Several different hierarchical watershed decompositions schemes have been described in the hydrology literature. One important such scheme is the Pfafstetter label method where each watershed is assigned a unique label and each grid cell is assigned a sequence of labels corresponding to the (nested) watersheds to which it belongs. In this paper we present an I/Oefficient algorithm for computing the Pfafstetter label of each cell of a grid terrain model. The algorithm uses O(sort(T)) I/Os,
External Memory Algorithms with Dynamically Changing Memory Allocations.
 DUKE UNIVERSITY
, 1998
"... We consider the problem of devising external memory algorithms whose memory allocations can change dynamically and unpredictably at runtime. The ..."
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Cited by 7 (3 self)
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We consider the problem of devising external memory algorithms whose memory allocations can change dynamically and unpredictably at runtime. The
Flow Computation on Massive Grids
, 2001
"... As detailed terrain data becomes available, GIS applications target larger geographic areas at finer resolutions. Processing the massive data presents significant challenges to GIS systems and demands algorithms that are optimized for both data movement and computation. In this paper we develop effi ..."
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Cited by 6 (2 self)
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As detailed terrain data becomes available, GIS applications target larger geographic areas at finer resolutions. Processing the massive data presents significant challenges to GIS systems and demands algorithms that are optimized for both data movement and computation. In this paper we develop efficient algorithms for flow routing on massive terrains, extending our previous work on flow accumulation. Our implementations of these algorithms constitute the first comprehensive terrain flow software system designed and optimized for massive data. We compare the performance of our system, called Terraflow, with that of state of the art commercial and opensource GIS systems. On large terrains, Terraflow outperforms existing systems by a factor of 2 to 1000, and is capable of solving problems of a scope and scale that are impractical with previous algorithms.
On computational models for flash memory devices
 in Experimental Algorithms, 2009
"... Abstract. Flash memorybased solidstate disks are fast becoming the dominant form of enduser storage devices, partly even replacing the traditional harddisks. Existing twolevel memory hierarchy models fail to realize the full potential of flashbased storage devices. We propose two new computati ..."
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Cited by 4 (1 self)
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Abstract. Flash memorybased solidstate disks are fast becoming the dominant form of enduser storage devices, partly even replacing the traditional harddisks. Existing twolevel memory hierarchy models fail to realize the full potential of flashbased storage devices. We propose two new computation models, the general flash model and the unitcost model, for memory hierarchies involving these devices. Our models are simple enough for meaningful algorithm design and analysis. In particular, we show that a broad range of existing externalmemory algorithms and data structures based on the merging paradigm can be adapted efficiently into the unitcost model. Our experiments show that the theoretical analysis of algorithms on our models corresponds to the empirical behavior of algorithms when using solidstate disks as external memory. 1
Fault Tolerant External Memory Algorithms
"... Abstract. Algorithms dealing with massive data sets are usually designed for I/Oefficiency, often captured by the I/O model by Aggarwal and Vitter. Another aspect of dealing with massive data is how to deal with memory faults, e.g. captured by the adversary based faulty memory RAM by Finocchi and I ..."
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Cited by 3 (2 self)
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Abstract. Algorithms dealing with massive data sets are usually designed for I/Oefficiency, often captured by the I/O model by Aggarwal and Vitter. Another aspect of dealing with massive data is how to deal with memory faults, e.g. captured by the adversary based faulty memory RAM by Finocchi and Italiano. However, current fault tolerant algorithms do not scale beyond the internal memory. In this paper we investigate for the first time the connection between I/Oefficiency in the I/O model and fault tolerance in the faulty memory RAM, and we assume that both memory and disk are unreliable. We show a lower bound on the number of I/Os required for any deterministic dictionary that is resilient to memory faults. We design a static and a dynamic deterministic dictionary with optimal query performance as well as an optimal sorting algorithm and an optimal priority queue. Finally, we consider scenarios where only cells in memory or only cells on disk are corruptible and separate randomized and deterministic dictionaries in the latter. 1
The Complexity of Flow on Fat Terrains and its I/OEfficient Computation
"... We study the complexity and the I/Oefficient computation of flow on triangulated terrains. We present an acyclic graph, the descent graph, that enables us to trace flow paths in triangulations i/oefficiently. We use the descent graph to obtain i/oefficient algorithms for computing river networks ..."
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We study the complexity and the I/Oefficient computation of flow on triangulated terrains. We present an acyclic graph, the descent graph, that enables us to trace flow paths in triangulations i/oefficiently. We use the descent graph to obtain i/oefficient algorithms for computing river networks and watershedarea maps in O(Sort(d + r)) i/o’s, where r is the complexity of the river network and d of the descent graph. Furthermore we describe a data structure based on the subdivision of the terrain induced by the edges of the triangulation and paths of steepest ascent and descent from its vertices. This data structure can be used to report the boundary of the watershed of a query point q or the flow path from q in O(l(s) + Scan(k)) i/o’s, where s is the complexity of the subdivision underlying the data structure, l(s) is the number of i/o’s used for planar point location in this subdivision, and k is the size of the reported output. On αfat terrains, that is, triangulated terrains where the minimum angle of any triangle is bounded from below by α, we show that the worstcase complexity of the descent graph and of any path of steepest descent is O(n/α 2), where n is the number of triangles in the terrain. The worstcase complexity of the river network and the abovementioned data structure on such terrains is O(n 2 /α 2). When α is a positive constant this improves the corresponding bounds for arbitrary terrains by a linear factor. We prove that similar bounds cannot be proven for Delaunay triangulations: these can have river networks of complexity Θ(n 3). 1
External Memory Geometric Data Structures, Handbook of Massive Data Sets
, 2002
"... Many modern applications store and process datasets much larger than the main memory of even stateoftheart highend machines. Thus massive and dynamically changing datasets often need to be stored in space efficient data structures on external storage devices such as disks. In such cases the Inpu ..."
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Cited by 2 (1 self)
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Many modern applications store and process datasets much larger than the main memory of even stateoftheart highend machines. Thus massive and dynamically changing datasets often need to be stored in space efficient data structures on external storage devices such as disks. In such cases the Input/Output (or