A Data Structure for Spatio-Temporal Databases

The advantages and applications of spatial mechanisms are well documented; however, there are very few being designed. The principal hinderance to the design of spatial mechanisms is the great difficulty involved in specifying spatial problems and in interpreting spatial solutions. Similarly, the development of spatial codes to implement these techniques is held back by the lack of means to easily visualize and verify solutions, particularly in the realm of relational databases. If spatial mechanisms are to be successful, the designer must be able to synthesize, analyse and evaluate, as well as load and extract information, using a single code representing a spatial structure. This entails the implementation of spatial relationships involving spatial data structures. It is with this in mind that the Canadian Hydrographic Service database group embarked on the development of a new type of spatial database structure based on the quadtree concept

2D adaptive grid-based image analysis approach for biological networks

The accurate analysis of biological networks, enabled by the precise capture of their individual components, can reveal important underlying biological principles. Efficient image processing techniques are required to precisely identify and quantify the networks from complex images. In this paper, we present a novel approach for a weighted and undirected graph-based network reconstruction and quantification from 2D images using an adaptive rectangular mesh refinement approach. The proposed approach is able to efficiently identify the organizational principles of the network, capturing the underlying network structure, and computing relevant network topological properties. We validate the proposed approach by comparing it with the state-of-the-art method

A Study of Energy and Locality Effects using Space-filling Curves

The cost of energy is becoming an increasingly important driver for the operating cost of HPC systems, adding yet another facet to the challenge of producing efficient code. In this paper, we investigate the energy implications of trading computation for locality using Hilbert and Morton space-filling curves with dense matrix-matrix multiplication. The advantage of these curves is that they exhibit an inherent tiling effect without requiring specific architecture tuning. By accessing the matrices in the order determined by the space-filling curves, we can trade computation for locality. The index computation overhead of the Morton curve is found to be balanced against its locality and energy efficiency, while the overhead of the Hilbert curve outweighs its improvements on our test system.Comment: Proceedings of the 2014 IEEE International Parallel & Distributed Processing Symposium Workshops (IPDPSW

Generation of Neuronal Trees by a New Three Letters Encoding

A neuronal tree is a rooted tree with n leaves whose each internal node has at least two children; this class not only is defined based on the structure of dendrites in neurons, but also refers to phylogenetic trees or evolutionary trees. More precisely, neuronal trees are rooted-multistate phylogenetic trees whose size is defined as the number of leaves. In this paper, a new encoding over an alphabet of size 3 (minimal cardinality) is introduced for representing the neuronal trees with a given number of leaves. This encoding is used for generating neuronal trees with n leaves in A-order with constant average time and O(n) time complexity in the worst case. Also, new ranking and unranking algorithms are presented in time complexity of O(n) and O(n log n), respectively

A distributed Quadtree Dictionary approach to multi-resolution visualization of scattered neutron data

Grid computing is described as dependable, seamless, pervasive access to resources and services, whereas mobile computing allows the movement of people from place to place while staying connected to resources at each location. Mobile grid computing is a new computing paradigm, which joins these two technologies by enabling access to the collection of resources within a user\u27s virtual organization while still maintaining the freedom of mobile computing through a service paradigm. A major problem in virtual organization is needs mismatch, in which one resources requests a service from another resources it is unable to fulfill, since virtual organizations are necessarily heterogeneous collections of resources. In this dissertation we propose a solution to the needs mismatch problem in the case of high energy physics data. Specifically, we propose a Quadtree Dictionary (QTD) algorithm to provide lossless, multi-resolution compression of datasets and enable their visualization on devices of all capabilities. As a prototype application, we extend the Integrated Spectral Analysis Workbench (ISAW) developed at the Intense Pulsed Neutron Source Division of the Argonne National Laboratory into a mobile Grid application, Mobile ISAW. In this dissertation we compare our QTD algorithm with several existing compression techniques on ISAW\u27s Single-Crystal Diffractometer (SCD) datasets. We then extend our QTD algorithm to a distributed setting and examine its effectiveness on the next generation of SCD datasets. In both a serial and distributed setting, our QTD algorithm performs no worse than existing techniques such as the square wavelet transform in terms of energy conservation, while providing the worst-case savings of 8:1

A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et al. [{\it Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes}, J. Comput. Phys. (2020)], to a fully-coupled, provably second-order accurate scheme in time, while maintaining energy-stability. The new method requires fewer matrix assemblies in each Newton iteration resulting in faster solution time. The method is based on a fully-implicit Crank-Nicolson scheme in time and a pressure stabilization for an equal order Galerkin formulation. That is, we use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) procedure to stabilize the pressure. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise, Rayleigh-Taylor instability, and lid-driven cavity flow problems. We analyze in detail the scaling of our numerical implementation.Comment: 48 pages, 18 figures, submitted to Computer Methods in Applied Mechanics and Engineerin

Approximate range searching☆☆A preliminary version of this paper appeared in the Proc. of the 11th Annual ACM Symp. on Computational Geometry, 1995, pp. 172–181.

AbstractThe range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges. In this paper we show that if one is willing to allow approximate ranges, then it is possible to do much better. In particular, given a bounded range Q of diameter w and ε>0, an approximate range query treats the range as a fuzzy object, meaning that points lying within distance εw of the boundary of Q either may or may not be counted. We show that in any fixed dimension d, a set of n points in Rd can be preprocessed in O(n+logn) time and O(n) space, such that approximate queries can be answered in O(logn(1/ε)d) time. The only assumption we make about ranges is that the intersection of a range and a d-dimensional cube can be answered in constant time (depending on dimension). For convex ranges, we tighten this to O(logn+(1/ε)d−1) time. We also present a lower bound for approximate range searching based on partition trees of Ω(logn+(1/ε)d−1), which implies optimality for convex ranges (assuming fixed dimensions). Finally, we give empirical evidence showing that allowing small relative errors can significantly improve query execution times

The Peano software---parallel, automaton-based, dynamically adaptive grid traversals

We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata—one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a “one way to implement things” code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software