Locality-aware parallel block-sparse matrix-matrix multiplication using the Chunks and Tasks programming model

We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A distributed quadtree matrix representation is straightforward to implement due to our recent development of the Chunks and Tasks programming model [Parallel Comput. 40, 328 (2014)]. The quadtree representation combined with the Chunks and Tasks model leads to favorable weak and strong scaling of the communication cost with the number of processes, as shown both theoretically and in numerical experiments. Matrices are represented by sparse quadtrees of chunk objects. The leaves in the hierarchy are block-sparse submatrices. Sparsity is dynamically detected by the matrix library and may occur at any level in the hierarchy and/or within the submatrix leaves. In case graphics processing units (GPUs) are available, both CPUs and GPUs are used for leaf-level multiplication work, thus making use of the full computing capacity of each node. The performance is evaluated for matrices with different sparsity structures, including examples from electronic structure calculations. Compared to methods that do not exploit data locality, our locality-aware approach reduces communication significantly, achieving essentially constant communication per node in weak scaling tests.Comment: 35 pages, 14 figure

Optimal Joins Using Compact Data Structures

Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality we either need to build completely new indexes, or we must populate the database with several instantiations of indexes such as B+-trees. Either way, this means spending an extra amount of storage space that may be non-negligible. We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quadtree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal

Pathfinding in hierarchical representation of large realistic virtual terrains

Pathfinding is critical to virtual simulation applications. One of the most prominent pathfinding challenges is the fast computation of path plans in large and realistic virtual terrain environments. To tackle this problem, this work proposes the exploration of a quadtree structure in the navigation map representation of large real-world virtual terrains. Exploring a hierarchical approach for virtual terrain representation, we detail how a global hierarchical pathfinding algorithm searches for a path in a coarse initial navigation map representation. Then, during execution time, the pathfinding algorithm refines regions of interest in this terrain representation in order to compute paths with a higher quality in areas where a large amount of navigation obstacles is found. The computational time of such hierarchical pathfinding algorithm is systematically measured in different hierarchical and non-hierarchical terrain representation structures that are instantiated in the modeling of a small real-world terrain scenario. Then, similar experiments are developed in a large real-world virtual terrain that is inserted in a real-life simulation system for the development of military tactical training exercises. The results show that the computational time required to generate pathfinding answers can be optimized when the proposed hierarchical pathfinding algorithm along with the easy and reliable implementation of the quadtree-based navigation map representation of the large virtual terrain are explored in the development of simulation systems

Quadtree Generating Networks: Efficient Hierarchical Scene Parsing with Sparse Convolutions

Semantic segmentation with Convolutional Neural Networks is a memory-intensive task due to the high spatial resolution of feature maps and output predictions. In this paper, we present Quadtree Generating Networks (QGNs), a novel approach able to drastically reduce the memory footprint of modern semantic segmentation networks. The key idea is to use quadtrees to represent the predictions and target segmentation masks instead of dense pixel grids. Our quadtree representation enables hierarchical processing of an input image, with the most computationally demanding layers only being used at regions in the image containing boundaries between classes. In addition, given a trained model, our representation enables flexible inference schemes to trade-off accuracy and computational cost, allowing the network to adapt in constrained situations such as embedded devices. We demonstrate the benefits of our approach on the Cityscapes, SUN-RGBD and ADE20k datasets. On Cityscapes, we obtain an relative 3% mIoU improvement compared to a dilated network with similar memory consumption; and only receive a 3% relative mIoU drop compared to a large dilated network, while reducing memory consumption by over 4$\times$.Comment: Accepted for IEEE Winter Conference on Applications of Computer Vision (WACV) 202

Quadtree based mouse trajectory analysis for efficacy evaluation of voice-enabled CAD

Voice-enabled applications have caught considerable research interest in recent years. It is generally believed that voice based interactions can improve the working efficiencies and the overall productivities. Quantitative evaluations on the performance boost by using such Human-Computer interactions (HCI) are therefore necessary to justify the claimed efficacies and the usefulness of the HCI system. In this paper, a quadtree based approach is proposed to analyze the mouse movement distributions in the proposed Voice-enabled Computer-Aided Design (VeCAD) system. The mouse tracker keeps a record of all the mouse movement during the solid modeling process, and a quadtree based approach is applied to analyze the mouse trajectory distributions in both the traditional CAD and the VeCAD system. Our experiments show that the mouse movement is significantly reduced when voice is used to activate CAD modeling commands. ©2009 IEEE.published_or_final_versionThe IEEE International Conference on Virtual Environments, Human-Computer Interfaces, and Measurements Systems (VECIMS) 2009, Hong Kong, 11-13 May 2009. In Conference Proceedings, 2009, p. 196-20

The Representation of symmetric patterns using the quadtree data structure

Hierarchical data structures for image representation have been widely explored in recent years. These data structures are based on the principle of recursive decomposition of an image region. The most commonly mentioned picture data structure for two-dimensional data is referred to as a quadtree . The purpose of this thesis is to investigate the use of a general quadtree scheme as a means of representing symmetric images. Specifically, images are generated according to the rules of selected two-dimensional plane symmetry groups

Algebraic topological analysis of time-sequence of digital images

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, each of them defined as 2D arrays of pixels. Our answer is based on an algebraic-topological coding, called AT–model, for a nD (n=2,3) digital binary-valued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT–models for all the 2D digital images in a time sequence, it is possible to get an AT–model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence. If the frames are represented in a quadtree format, a similar positive result can be derived