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Towards Optimal Locality in MeshIndexings
, 1997
"... The efficiency of many data structures and algorithms relies on "localitypreserving" indexing schemes for meshes. We concentrate on the case in which the maximal distance between two mesh nodes indexed i and j shall be a slowgrowing function of ji jj. We present a new 2D indexing scheme we call H ..."
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Cited by 31 (4 self)
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The efficiency of many data structures and algorithms relies on "localitypreserving" indexing schemes for meshes. We concentrate on the case in which the maximal distance between two mesh nodes indexed i and j shall be a slowgrowing function of ji jj. We present a new 2D indexing scheme we call Hindexing , which has superior (possibly optimal) locality in comparison with the wellknown Hilbert indexings. Hindexings form a Hamiltonian cycle and we prove that they are optimally localitypreserving among all cyclic indexings. We provide fairly tight lower bounds for indexings without any restriction. Finally, illustrated by investigations concerning 2D and 3D Hilbert indexings, we present a framework for mechanizing upper bound proofs for locality.
The Application of Spacefilling Curves to the Storage and Retrieval of Multidimensional Data
, 2000
"... Indexing of multidimensional data has been the focus of a considerable amount of research effort over many years but no generally agreed paradigm has emerged to compare with the impact of the BTree, for example, on the indexing of onedimensional data. At the same time, the need for efficient meth ..."
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Cited by 16 (3 self)
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Indexing of multidimensional data has been the focus of a considerable amount of research effort over many years but no generally agreed paradigm has emerged to compare with the impact of the BTree, for example, on the indexing of onedimensional data. At the same time, the need for efficient methods is ever more important in an environment where databases become larger and more complex in their structures. Mapping multidimensional data to one dimension, thus enabling onedimensional access methods to be exploited, has been suggested in the literature but for the most part interest has been confined to the Zorder curve. The possibility of using other curves, such as the Hilbert and Graycode curves, whose characteristics differ from those of the Zorder curve, has also been suggested. In this thesis we design and implement a working le store which is underpinned by the principle of mapping multidimensional data to one of a variety of spacefilling curves and their variants. Data is then indexed using a B+ Tree which remains compact, regardless of the volume and number of dimensions. The implementation has entailed developing
Processor Allocation on Cplant: Achieving General Processor Locality Using OneDimensional Allocation Strategies
 In Proc. 4th IEEE International Conference on Cluster Computing
, 2002
"... The Computational Plant or Cplant is a commoditybased supercomputer under development at Sandia National Laboratories. This paper describes resourceallocation strategies to achieve processor locality for parallel jobs in Cplant and other supercomputers. Users of Cplant and other Sandia supercomput ..."
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Cited by 10 (2 self)
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The Computational Plant or Cplant is a commoditybased supercomputer under development at Sandia National Laboratories. This paper describes resourceallocation strategies to achieve processor locality for parallel jobs in Cplant and other supercomputers. Users of Cplant and other Sandia supercomputers submit parallel jobs to a job queue. When a job is scheduled to run, it is assigned to a set of processors. To obtain maximum throughput, jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs.
Graph Partitioning in Scientific Simulations: Multilevel Schemes versus SpaceFilling Curves
"... Using spacefilling curves to partition unstructured finite element meshes is a widely applied strategy when it comes to distributing load among several computation nodes. Compared to more elaborated graph partitioning packages, this geometric approach is relatively easy to implement and very fast. ..."
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Cited by 6 (3 self)
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Using spacefilling curves to partition unstructured finite element meshes is a widely applied strategy when it comes to distributing load among several computation nodes. Compared to more elaborated graph partitioning packages, this geometric approach is relatively easy to implement and very fast. However, results are not expected to be as good as those of the latter, but no detailed comparison has ever been published. In this paper we will...
Algorithmic Support for CommodityBased Parallel Computing Systems
, 2003
"... Follows Abstract The Computational Plant or Cplant is a commoditybased distributedmemory supercomputer under development at Sandia National Laboratories. ..."
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Cited by 2 (2 self)
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Follows Abstract The Computational Plant or Cplant is a commoditybased distributedmemory supercomputer under development at Sandia National Laboratories.
Communication Patterns and Allocation Strategies
 In Proc. 3rd Int. Workshop on Performance Modeling, Evaluation, and Optimization of Parallel and Distributed Systems
, 2004
"... Motivated by observations about job runtimes on the CPlant system, we use a tracedriven microsimulator to begin characterizing the performance of di#erent classes of allocation algorithms on jobs with di#erent communication patterns in spaceshared parallel systems with mesh topology. We show th ..."
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Cited by 1 (1 self)
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Motivated by observations about job runtimes on the CPlant system, we use a tracedriven microsimulator to begin characterizing the performance of di#erent classes of allocation algorithms on jobs with di#erent communication patterns in spaceshared parallel systems with mesh topology. We show that relative performance varies considerably with communication pattern. The Paging strategy using the Hilbert spacefilling curve and the Best Fit heuristic performed best across several communication patterns.
On sampling in higherdimensional peertopeer systems
 IN PROCEEDINGS OF LATIN AMERICAN THEORETICAL INFORMATICS (LATIN 2006), LNCS 3887
, 2006
"... We present fully distributed algorithms for random sampling of nodes in peertopeer systems, extending and generalizing the work of King and Saia [Proceedings of PODC 2004] from simple Chordlike distributed hash tables to systems based on higherdimensional hierarchical constructions, like Conte ..."
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Cited by 1 (0 self)
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We present fully distributed algorithms for random sampling of nodes in peertopeer systems, extending and generalizing the work of King and Saia [Proceedings of PODC 2004] from simple Chordlike distributed hash tables to systems based on higherdimensional hierarchical constructions, like Content Addressable Networks (CAN). We also show preliminary results on the generalization of the problem to biased sampling. In addition, we provide an extension of CAN that requires only O(1) space per node and achieves O(log n) lookup latency and message complexities.
A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization
"... Sparse grids are an efficient approximation method for functions, especially in higher dimensions d 3. Compared to regular, uniform grids of a mesh parameter h, which contain h \Gammad points in d dimensions, sparse grids require only h \Gamma1 j log hj d\Gamma1 points due to a truncated, ten ..."
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Sparse grids are an efficient approximation method for functions, especially in higher dimensions d 3. Compared to regular, uniform grids of a mesh parameter h, which contain h \Gammad points in d dimensions, sparse grids require only h \Gamma1 j log hj d\Gamma1 points due to a truncated, tensorproduct multiscale basis representation. The purpose of this paper is to survey some activities for the solution of partial differential equations with methods based sparse grid. Furthermore some aspects of sparse grids are discussed such as adaptive grid refinement, parallel computing, a spacetime discretization scheme and the structure of a code to implement these methods. 1.1 Introduction Quite lot of phenomena in science and engineering can be modeled by boundary value problems of ordinary differential equation or partial differential equation type. Further assumptions to simplify the model like axisand radialsymmetries often give rise to a PDE in one or two dimensions (d = 1; 2), ...
Effectiveness of Landmark Analysis for Establishing Locality in P2P Networks
 THE SECOND INTERNATIONAL CONFERENCE ON ADVANCES IN P2P SYSTEMS (AP2PS 2010), OCTOBER 2530, 2010, FLORENCE, ITALY.
, 2010
"... Locality to other nodes on a peertopeer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multidimensional feature vector. Each peer node uses th ..."
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Locality to other nodes on a peertopeer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multidimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and nonlinear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical powerlaw distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.