Rectilinear partitioning of irregular data parallel computations

New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed

Automating Topology Aware Mapping for Supercomputers

Petascale machines with hundreds of thousands of cores are being built. These machines have varying interconnect topologies and large network diameters. Computation is cheap and communication on the network is becoming the bottleneck for scaling of parallel applications. Network contention, specifically, is becoming an increasingly important factor affecting overall performance. The broad goal of this dissertation is performance optimization of parallel applications through reduction of network contention. Most parallel applications have a certain communication topology. Mapping of tasks in a parallel application based on their communication graph, to the physical processors on a machine can potentially lead to performance improvements. Mapping of the communication graph for an application on to the interconnect topology of a machine while trying to localize communication is the research problem under consideration. The farther different messages travel on the network, greater is the chance of resource sharing between messages. This can create contention on the network for networks commonly used today. Evaluative studies in this dissertation show that on IBM Blue Gene and Cray XT machines, message latencies can be severely affected under contention. Realizing this fact, application developers have started paying attention to the mapping of tasks to physical processors to minimize contention. Placement of communicating tasks on nearby physical processors can minimize the distance traveled by messages and reduce the chances of contention. Performance improvements through topology aware placement for applications such as NAMD and OpenAtom are used to motivate this work. Building on these ideas, the dissertation proposes algorithms and techniques for automatic mapping of parallel applications to relieve the application developers of this burden. The effect of contention on message latencies is studied in depth to guide the design of mapping algorithms. The hop-bytes metric is proposed for the evaluation of mapping algorithms as a better metric than the previously used maximum dilation metric. The main focus of this dissertation is on developing topology aware mapping algorithms for parallel applications with regular and irregular communication patterns. The automatic mapping framework is a suite of such algorithms with capabilities to choose the best mapping for a problem with a given communication graph. The dissertation also briefly discusses completely distributed mapping techniques which will be imperative for machines of the future.published or submitted for publicationnot peer reviewe

Image-space decomposition algorithms for sort-first parallel volume rendering of unstructured grids

Twelve adaptive image-space decomposition algorithms are presented for sort-first parallel direct volume rendering (DVR) of unstructured grids on distributed-memory architectures. The algorithms are presented under a novel taxonomy based on the dimension of the screen decomposition, the dimension of the workload arrays used in the decomposition, and the scheme used for workload-array creation and querying the workload of a region. For the 2D decomposition schemes using 2D workload arrays, a novel scheme is proposed to query the exact number of screen-space bounding boxes of the primitives in a screen region in constant time. A probe-based chains-on-chains partitioning algorithm is exploited for load balancing in optimal 1D decomposition and iterative 2D rectilinear decomposition (RD). A new probe-based optimal 2D jagged decomposition (OJD) is proposed which is much faster than the dynamic-programming based OJD scheme proposed in the literature. The summed-area table is successfully exploited to query the workload of a rectangular region in constant time in both OJD and RD schemes for the subdivision of general 2D workload arrays. Two orthogonal recursive bisection (ORB) variants are adapted to relax the straight-line division restriction in conventional ORB through using the medians-of-medians approach on regular mesh and quadtree superimposed on the screen. Two approaches based on the Hilbert space-filling curve and graph-partitioning are also proposed. An efficient primitive classification scheme is proposed for redistribution in 1D, and 2D rectilinear and jagged decompositions. The performance comparison of the decomposition algorithms is modeled by establishing appropriate quality measures for load-balancing, amount of primitive replication and parallel execution time. The experimental results on a Parsytec CC system using a set of benchmark volumetric datasets verify the validity of the proposed performance models. The performance evaluation of the decomposition algorithms is also carried out through the sort-first parallelization of an efficient DVR algorithm

Sparse matrix decomposition with optimal load balancing

Optimal load balancing in sparse matrix decomposition without disturbing the row/column ordering is investigated. Both asymptotically and run-time efficient exact algorithms are proposed and implemented for one-dimensional (1D) striping and two-dimensional (2D) jagged partitioning. Binary search method is successfully adopted to 1D striped decomposition by deriving and exploiting a good upper bound on the value of an optimal solution. A binary search algorithm is proposed for 2D jagged partitioning by introducing a new 2D probing scheme. A new iterative-refinement scheme is proposed for both 1D and 2D partitioning. Proposed algorithms are also space efficient since they only need the conventional compressed storage scheme for the given matrix, avoiding the need for a dense workload matrix in 2D decomposition. Experimental results on a wide set of test matrices show that considerably better decompositions can be obtained by using optimal load balancing algorithms instead of heuristics. Proposed algorithms are 100 times faster than a single sparse-matrix vector multiplication (SpMxV), in the 64-way 1D decompositions, on the overall average. Our jagged partitioning algorithms are only 60% slower than a single SpMxV computation in the 8×8-way 2D decompositions, on the overall average

Semiannual final report, 1 October 1991 - 31 March 1992

A summary of research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period 1 Oct. 1991 through 31 Mar. 1992 is presented

Data Assimilation for Wildland Fires: Ensemble Kalman filters in coupled atmosphere-surface models

Two wildland fire models are described, one based on reaction-diffusion-convection partial differential equations, and one based on semi-empirical fire spread by the level let method. The level set method model is coupled with the Weather Research and Forecasting (WRF) atmospheric model. The regularized and the morphing ensemble Kalman filter are used for data assimilation.Comment: Minor revision, except description of the model expanded. 29 pages, 9 figures, 53 reference