External-memory computational geometry

Goodrich, Michael T.; Tsay, Jyh-Jong; Vengroff, Darren Erik; Vitter, Jeffrey Scott

doi:10.1109/sfcs.1993.366816

Cited by 129 publications

(121 citation statements)

References 28 publications

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“…Aggarwal and Vitter [1] introduced the external memory model (see also [5,16,27]), which counts the number of block I/Os to and from external memory. They also describe a parallel disk model (PDM), where D blocks can simultaneously be read or written from/to D different disks, however, they do not consider multiple processors.…”

Section: Introductionmentioning

confidence: 99%

Fundamental parallel algorithms for private-cache chip multiprocessors

Arge

Goodrich

Nelson

et al. 2008

Proceedings of the Twentieth Annual Symposium on Parallelism in Algorithms and Architectures

134

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In this paper, we study parallel algorithms for private-cache chip multiprocessors (CMPs), focusing on methods for foundational problems that can scale to hundreds or even thousands of cores. By focusing on private-cache CMPs, we show that we can design efficient algorithms that need no additional assumptions about the way that cores are interconnected, for we assume that all inter-processor communication occurs through the memory hierarchy. We study several fundamental problems, including prefix sums, selection, and sorting, which often form the building blocks of other parallel algorithms. Indeed, we present two sorting algorithms, a distribution sort and a mergesort. All algorithms in the paper are asymptotically optimal in terms of the parallel cache accesses and space complexity under reasonable assumptions about the relationships between the number of processors, the size of memory, and the size of cache blocks. In addition, we study sorting lower bounds in a computational model, which we call the parallel external-memory (PEM) model, that formalizes the essential properties of our algorithms for private-cache chip multiprocessors.

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Section: Introductionmentioning

confidence: 99%

Fundamental parallel algorithms for private-cache chip multiprocessors

Arge

Goodrich

Nelson

et al. 2008

Proceedings of the Twentieth Annual Symposium on Parallelism in Algorithms and Architectures

134

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“…They gave upper and lower bounds on the number of I/Os for several fundamental problems including sorting, selection, matrix transposition, and FFT. Following their work, researchers have designed I/O-optimal algorithms for fundamental problems in graph theory [13] and computational geometry [21]. The problem of sorting has been a focus of attention, resulting in our better understanding about the I/O complexity of sorting [8].…”

Section: Related Workmentioning

confidence: 99%

Cache-efficient matrix transposition

Chatterjee

Sen

Proceedings Sixth International Symposium on High-Performance Computer Architecture. HPCA-6 (Cat. No.PR00550)

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We investigate the memory system performance of several algorithms for transposing an N N matrix in-place, where N is large. Specifically, we investigate the relative contributions of the data cache, the translation lookaside buffer, register tiling, and the array layout function to the overall running time of the algorithms. We use various memory models to capture and analyze the effect of various facets of cache memory architecture that guide the choice of a particular algorithm, and attempt to experimentally validate the predictions of the model. Our major conclusions are as follows: limited associativity in the mapping from main memory addresses to cache sets can significantly degrade running time; the limited number of TLB entries can easily lead to thrashing; the fanciest optimal algorithms are not competitive on real machines even at fairly large problem sizes unless cache miss penalties are quite high; low-level performance tuning "hacks", such as register tiling and array alignment, can significantly distort the effects of improved algorithms; and hierarchical nonlinear layouts are inherently superior to the standard This work is supported in part by DARPA Grant DABT63-98-1-0001, NSF Grants CDA-97-2637 and CDA-95-12356, The University of North Carolina at Chapel Hill, Duke University, and an equipment donation through Intel Corporation's Technology for Education 2000 Program. The views and conclusions contained herein are those of the authors and should not be interpreted as representing the official policies or endorsements, either expressed or implied, of DARPA or the U.S. Government. canonical layouts (such as row-or column-major) for this problem.

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“…Although popular in computational geometry literature [31], the closest pair problem has not gained special attention is spatial database research. Certain other problems of computational geometry, including the ''all nearest neighbor'' problem (that is related to the closest pair problem), have been solved for external memory systems [17]. To the best of the authorsÕ knowledge, [8,21,33] are the only references to this type of queries.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Algorithms for processing K-closest-pair queries in spatial databases

Corral

Manolopoulos

Theodoridis

et al. 2004

Data & Knowledge Engineering

101

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This paper addresses the problem of finding the K closest pairs between two spatial datasets (the socalled, K closest pairs query, K-CPQ), where each dataset is stored in an R-tree. There are two different techniques for solving this kind of distance-based query. The first technique is the incremental approach, which returns the output elements one-by-one in ascending order of distance. The second one is the nonincremental alternative, which returns the K elements of the result all together at the end of the algorithm. In this paper, based on distance functions between two MBRs in the multidimensional Euclidean space, we propose a pruning heuristic and two updating strategies for minimizing the pruning distance, and use them in the design of three non-incremental branch-and-bound algorithms for K-CPQ between spatial objects stored in two R-trees. Two of those approaches are recursive following a Depth-First searching strategy and one is iterative obeying a Best-First traversal policy. The plane-sweep method and the search ordering are used as optimization techniques for improving the naive approaches. Besides, a number of interesting extensions of the K-CPQ (K-Self-CPQ, Semi-CPQ, K-FPQ (the K-farthest pairs query), etc.) are discussed. An extensive performance study is also presented. This study is based on experiments performed with real datasets. A wide range of values for the basic parameters affecting the performance of the algorithms is examined in order to designate the most efficient algorithm for each setting of parameter values. Finally, an experimental study of the behavior of the proposed K-CPQ branch-and-bound algorithms in terms of scalability of the dataset size and the K value is also included.

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External-memory computational geometry

Cited by 129 publications

References 28 publications

Fundamental parallel algorithms for private-cache chip multiprocessors

Fundamental parallel algorithms for private-cache chip multiprocessors

Cache-efficient matrix transposition

Algorithms for processing K-closest-pair queries in spatial databases

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