Orders Of Magnitude Speedup Research Articles

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracy by making use of averaging in the Random Noise coupling technique.

Solvated and generalised Born calculations differences using GPU CUDA and multi-CPU simulations of an antifreeze protein with AMBER

While there has been an increase in the number of biomolecular computational studies employing graphics processing units (GPU), results describing their use with the molecular dynamics package AMBER with the CUDA implementation are scarce. No information is available comparing MD methodologies pmemd.cuda, pmemd.mpi or sander.mpi, available in AMBER, for generalised Born (GB) simulations or with solvated systems. As part of our current studies with antifreeze proteins (AFP), and for the previous reasons, we present details of our experience comparing performance of MD simulations at varied temperatures between multi-CPU runs using sander.mpi, pmemd.mpi and pmemd.cuda with the AFP from the fish ocean pout (1KDF). We found extremely small differences in total energies between multi-CPU and GPU CUDA implementations of AMBER12 in 1ns production simulations of the solvated system using the TIP3P water model. Additionally, GPU computations achieved typical one order of magnitude speedups when using mixed precision but were similar to CPU speeds when computing with double precision. However, we found that GB calculations were highly sensitive to the choice of initial GB parametrisation regardless of the type of methodology, with substantial differences in total energies.

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

Accurate Modeling of Nonideal Low-Power PWM DC-DC Converters Operating in CCM and DCM using Enhanced Circuit-Averaging Techniques

The development of enhanced modeling techniques for the simulation of switched-mode Pulse Width Modulated (PWM) DC-DC power converters using circuit averaging is the main focus of this article. The circuit-averaging technique has traditionally been used to model the behavior of PWM DC-DC converters without considering important nonideal characteristics of the switching devices. As a result, most of these existing approaches present simplified models that are ideal or linearized, and do not accurately account for the performance characteristics of the converter. This is especially problematic for low-power applications. In this article, we present an enhanced nonideal behavioral circuit-averaged model that makes the simulation of DC-DC converters both computationally efficient and accurate, thereby presenting an important tool for circuit designers. Experimentally, we show that our Verilog-A-based new model allows for accurate simulation of both Buck- and Boost-type PWM converters operating in either CCM or DCM modes while providing more than one order of magnitude speedup over the transistor-level simulation.

Biomedical Ontology Quality Assurance Using a Big Data Approach

This article presents recent progresses made in using scalable cloud computing environment, Hadoop and MapReduce, to perform ontology quality assurance (OQA), and points to areas of future opportunity. The standard sequential approach used for implementing OQA methods can take weeks if not months for exhaustive analyses for large biomedical ontological systems. With OQA methods newly implemented using massively parallel algorithms in the MapReduce framework, several orders of magnitude in speed-up can be achieved (e.g., from three months to three hours). Such dramatically reduced time makes it feasible not only to perform exhaustive structural analysis of large ontological hierarchies, but also to systematically track structural changes between versions for evolutional analysis. As an exemplar, progress is reported in using MapReduce to perform evolutional analysis and visualization on the Systemized Nomenclature of Medicine—Clinical Terms (SNOMED CT), a prominent clinical terminology system. Future opportunities in three areas are described: one is to extend the scope of MapReduce-based approach to existing OQA methods, especially for automated exhaustive structural analysis. The second is to apply our proposed MapReduce Pipeline for Lattice-based Evaluation (MaPLE) approach, demonstrated as an exemplar method for SNOMED CT, to other biomedical ontologies. The third area is to develop interfaces for reviewing results obtained by OQA methods and for visualizing ontological alignment and evolution, which can also take advantage of cloud computing technology to systematically pre-compute computationally intensive jobs in order to increase performance during user interactions with the visualization interface. Advances in these directions are expected to better support the ontological engineering lifecycle.

Fast and Exact Fiber Surfaces for Tetrahedral Meshes.

Isosurfaces are fundamental geometrical objects for the analysis and visualization of volumetric scalar fields. Recent work has generalized them to bivariate volumetric fields with fiber surfaces, the pre-image of polygons in range space. However, the existing algorithm for their computation is approximate, and is limited to closed polygons. Moreover, its runtime performance does not allow instantaneous updates of the fiber surfaces upon user edits of the polygons. Overall, these limitations prevent a reliable and interactive exploration of the space of fiber surfaces. This paper introduces the first algorithm for the exact computation of fiber surfaces in tetrahedral meshes. It assumes no restriction on the topology of the input polygon, handles degenerate cases and better captures sharp features induced by polygon bends. The algorithm also allows visualization of individual fibers on the output surface, better illustrating their relationship with data features in range space. To enable truly interactive exploration sessions, we further improve the runtime performance of this algorithm. In particular, we show that it is trivially parallelizable and that it scales nearly linearly with the number of cores. Further, we study acceleration data-structures both in geometrical domain and range space and we show how to generalize interval trees used in isosurface extraction to fiber surface extraction. Experiments demonstrate the superiority of our algorithm over previous work, both in terms of accuracy and running time, with up to two orders of magnitude speedups. This improvement enables interactive edits of range polygons with instantaneous updates of the fiber surface for exploration purpose. A VTK-based reference implementation is provided as additional material to reproduce our results.

A GPU-based Soft Real-Time System for Simultaneous EEG Processing and Visualization

EEG processing is generally acknowledged as a computationally very intensive task. The execution of pre-processing steps, frequency domain operations and source localisation algorithms result in long execution times, which prohibit the use of high-resolution EEG brain imaging techniques outside research laboratory settings. We present a novel GPU-based streaming architecture, which has the potential to drastically reduce execution times and, at the same time, provide simultaneous 2D and 3D visualization facilities. The system uses a highly-optimised and re-configurable pipeline of CPU and GPU cores that attempts to exploit the tremendous computing power whenever possible. The system can process live data arriving from an EEG device or data stored in EEG data files. The computer drives a large display wall system consisting of four 46-inch monitors, which provides a 4K-resolution drawing surface for visualising raw EEG data, potential maps and various 3D views of the patient head. Two example brain imaging algorithms, the surface Laplacian and the spherical forward solution are used as an illustration for the effective use of the massively parallel GPU hardware in speeding up computations. The paper describes the architecture of the system, the key design decisions, and the performance optimization steps that were required to achieve sub-millisecond per-sample execution times. The control ow of the system is expressed in a very modular fashion in Java but the performance-critical algorithms are programmed in CUDA and run on the GPU. Relying on the CUDA-OpenGL interoperability bridge, the computing subsystem feeds visualisation results directly into the OpenGL pipeline, eliminating unnecessary GPU-Host data transfers. The system demonstrates that up to three orders of magnitude speedups are achievable compared to MATLAB implementations, and this processing speed can be maintained during simultaneous interactive 3D visualisation of the results.

ICE-COLA: towards fast and accurate synthetic galaxy catalogues optimizing a quasi-N-body method

Next generation galaxy surveys demand the development of massive ensembles of galaxy mocks to model the observables and their covariances, what is computationally prohibitive using $N$-body simulations. COLA is a novel method designed to make this feasible by following an approximate dynamics but with up to 3 orders of magnitude speed-ups when compared to an exact $N$-body. In this paper we investigate the optimization of the code parameters in the compromise between computational cost and recovered accuracy in observables such as two-point clustering and halo abundance. We benchmark those observables with a state-of-the-art $N$-body run, the MICE Grand Challenge simulation (MICE-GC). We find that using 40 time steps linearly spaced since $z_i \sim 20$, and a force mesh resolution three times finer than that of the number of particles, yields a matter power spectrum within $1\%$ for $k \lesssim 1\,h {\rm Mpc}^{-1}$ and a halo mass function within $5\%$ of those in the $N$-body. In turn the halo bias is accurate within $2\%$ for $k \lesssim 0.7\,h {\rm Mpc}^{-1}$ whereas, in redshift space, the halo monopole and quadrupole are within $4\%$ for $k \lesssim 0.4\,h {\rm Mpc}^{-1}$. These results hold for a broad range in redshift ($0 < z < 1$) and for all halo mass bins investigated ($M > 10^{12.5} \, h^{-1} \, {\rm M_{\odot}}$). To bring accuracy in clustering to one percent level we study various methods that re-calibrate halo masses and/or velocities. We thus propose an optimized choice of COLA code parameters as a powerful tool to optimally exploit future galaxy surveys.

(Invited) Comprehensive Assessment of Oxide Memristors As Post-CMOS Memory and Logic Devices

As modern field effect transistors (FETs) scale down into the sub-10-nm regime, the approaching end of CMOS scaling becomes evident. Recently, we have performed a series of three-dimensional, fully quantum-mechanical, charge-self-consistent transport simulations and optimizations to show [1] that all FETs, irrespective of their channel material, will reach a fundamental downscaling limit around 4-5 nm technology node, due to unacceptably high levels of thermally induced errors. To investigate alternatives to FET/CMOS scaling, many emerging devices and technologies have been under active research in recent years. Among them, oxide-based memristors have become one of the strongest candidates to replace flash, and possibly DRAM and SRAM in the near future [2]. Moreover, memristors have a high potential to enable beyond-CMOS technology advances in novel architectures for high performance computing [3]. However, despite the spectacular progress in experimental demonstration of oxide memristors, their microscopic transport theory and even some key operational principles, essential to advance experimental progress, remain uncertain [4]. To facilitate the understanding of physical switching mechanisms and accelerate experimental development in oxide memristors, we have developed a 3D fully-coupled electrical and thermal transport model [5] that solves simultaneously the time-dependent continuity equations for electrons, holes, and oxygen vacancies, the time-dependent heat equation including Joule heating sources, and the Poisson equation for all the charged species. The model captures all the most important processes that drive memristive switching, including field drift due to the electrical potential gradient, Fick diffusion due to the concentration gradient, and the Soret effect due to the temperature gradient. To properly simulate the movement of oxygen vacancies, the rigid point ion model [5] is used, in which the vacancy velocity exponentially depends on the temperature and the electric field when the field exceeds a critical value. The fully-coupled equations and relevant physical models are implemented in CHARON, a multi-dimensional parallel TCAD code developed at Sandia National Labs. CHARONis built upon the open-source Trilinos packages [6], which support finite element and finite volume discretization methods, state-of-the-art nonlinear and linear solvers, MPI parallel capability, and many more. It can simulate arbitrary device geometry and supports multi-physics capability (i.e., allowing for solving different equations in different regions). The coupled model has been applied to simulate the switching process in a 3D filamentary tantalum oxide memristor shown in Fig. 1(a). The layer material and thickness come from an experimental device published in Ref. [7]. Making use of the multi-physics capability in CHARON, we solve the coupled Poisson, electron, oxygen vacancy, and heat equations in the active Ta and conduction filament (CF) regions, with vacancies confined in Ta and CF regions, while in the Pt and Ta2O5 regions, due to absence of mobile vacancies, the coupled Poisson, electron, and heat equations are solved, with Pt treated as a highly doped n-type semiconductor using immobile dopants, and Ta2O5 as an undoped semiconductor. Extensive simulations show that both field drift and thermal processes play crucial roles in determining the switching dynamics of the bipolar TaOx device. Specifically, (i) during OFF switching, when a sufficient negative voltage is applied to the top Pt electrode, Joule heating causes the increase of temperature with the hottest spot located in the CF, and consequently, oxygen vacancies move away from CF into Ta under the influence of both heating and field, which leads to a vacancy density gap and possible depletion of vacancies in the entire CF at high negative voltage, resulting in the OFF state; (ii) during ON switching, a sufficient positive voltage causes Joule heating and the increase of temperature, and increased temperature causes vacancies moving from Ta into CF to refill the vacancy gap, resulting in the ON state. Interestingly, we show that the thermally activated field-dominated switching in the considered devices can lead to more than three orders of magnitude speed-up in switching time, with only 50% voltage/current increase. Simulated resistances during OFF and ON switching as a function of time and voltage show very good qualitative agreement with experimental measurement in Ref. [7]. Furthermore, under a triangular voltage sweep, the simulated current-voltage hysteresis curve is shown in Fig. 1(b), which also shows good qualitative agreement with the measured data in Ref. [8]. The generality of the proposed model allows to simulate and investigate the underlying physical switching mechanisms in a wide spectrum of oxide memristors ranging from field-dominant, field-thermal-driven to thermal-dominant memristive devices. Figure 1

Gunrock

For large-scale graph analytics on the GPU, the irregularity of data access/control flow and the complexity of programming GPUs have been two significant challenges for developing a programmable high-performance graph library. "Gunrock," our high-level bulk-synchronous graph-processing system targeting the GPU, takes a new approach to abstracting GPU graph analytics: rather than designing an abstraction around computation , Gunrock instead implements a novel data-centric abstraction centered on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high-performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We evaluate Gunrock on five graph primitives (BFS, BC, SSSP, CC, and PageRank) and show that Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives, and better performance than any other GPU high-level graph library.

A Fast Method for Computing Chemical Potentials and Phase Equilibria of Macromolecular Mixtures

Chemical potential is a fundamental property for determining thermodynamic equilibria involving exchanges of molecules, such as between two phases of molecular systems. Previously we developed the FMAP method for calculating excess chemical potentials according to Widom insertion [1, 2]. Intermolecular interaction energies were expressed as correlation times and evaluated via fast Fourier transform. Here we extend this method to calculate phase equilibria. Chemical potentials are calculated by FMAP at a wide range of molecular densities and the boundary between low- and high-density phases is identified by the Maxwell equal-area rule. When benchmarked on a Lennard-Jones fluid, our method produces an accurate phase diagram at 10% of the computational cost of the present best method. Importantly, the gain in computational speed increases dramatically as the molecules become more complex, potentially reaching many orders of magnitude in speedup for atomistically represented proteins [2]. Our method thus opens the door to accurate determination of phase equilibria for macromolecular mixtures. Of particular interest are protein-protein mixtures and protein-RNA mixtures that involve poly-valent interactions. These mixtures are known to undergo a liquid-liquid phase separation, both in vitro and in vivo. Our phase calculations for these systems will lead to much need physical understanding of the liquid-liquid phase separation and how it is used for many biological functions. 1. Qin, S., Zhou, H. X. J. Chem. Theory Comput. 2013, 9, 4633−4643. 2. Qin, S., Zhou, H. X. J. Chem. Theory Comput. 2014, 10, 2824-2835.

Noise Margin Modeling for Zero-$V_{\text {GS}}$ Load TFT Circuits and Yield Estimation

The flexible electronics is promising in the area of the Internet of Things and wearable devices and the thin-film transistor (TFT) technologies are crucial for flexible electronics. Among them, the zero- $V_{\text {GS}}$ load TFT circuits are widely used for its simple structure and high gain merits. However, the yield model is lacking for zero- $V_{\text {GS}}$ load TFT circuits. In this paper, the analytical noise margin model for the zero- $V_{\text {GS}}$ load TFT NAND gate and NOR gate is derived. Based on that, a simple, accurate, and highly scalable yield model for the combinational TFT logic circuits based on standard cell library is further proposed. ISCAS’85 benchmark circuits are used to validate the yield model. Compared with Monte Carlo simulation, the model achieves 3–4 orders of magnitude speedup with comparative results.

Performance Boosting of Flexible ZnO UV Sensors with Rational Designed Absorbing Antireflection Layer and Humectant Encapsulation.

Flexible ZnO thin film UV sensors with 3 orders of magnitude improvement in sensitivity and 2 orders of magnitude acceleration in speed are realized via light absorption efficiency enhancement and surface encapsulation. Devices are constructed on polyethylene substrate incorporating morphology controlled ZnO nanorod arrays (NRAs) as absorbing antireflection layers. By adjusting the morphology of ZnO NRAs, the light absorptance exceeds 99% through effectively trapping incident photons. As a result, the sensitivity of the UV sensor reaches 109 000. Moreover, a mechanism of competitive chemisorption between O2 and H2O at oxygen vacancy sites is proposed to explain the phenomenon of the speed acceleration in moist environment. A new approach of humectant encapsulation is used to make H2O participant rapid processes dominant for speed acceleration. Two orders of magnitude speed enhancement in reset time is achieved by polyethylene glycol encapsulation. After a total 3000 cycles bending test, the decay in the responsivity of UV sensor is within 20%, indicating good mechanical stability. All these results not only demonstrate a simple, effective and scalable approach to fabricate high sensitive and fast response flexible ZnO UV sensors, but also provide meaningful references for performance boosting of photoelectronic devices based on other oxide semiconductors.

The similarity-aware relational database set operators

Identifying similarities in large datasets is an essential operation in several applications such as bioinformatics, pattern recognition, and data integration. To make a relational database management system similarity-aware, the core relational operators have to be extended. While similarity-awareness has been introduced in database engines for relational operators such as joins and group-by, little has been achieved for relational set operators, namely Intersection, Difference, and Union. In this paper, we propose to extend the semantics of relational set operators to take into account the similarity of values. We develop efficient query processing algorithms for evaluating them, and implement these operators inside an open-source database system, namely PostgreSQL. By extending several queries from the TPC-H benchmark to include predicates that involve similarity-based set operators, we perform extensive experiments that demonstrate up to three orders of magnitude speedup in performance over equivalent queries that only employ regular operators.

Parallel construction of classification trees on a GPU

SummaryAlgorithms for constructing tree‐based classifiers are aimed at building an optimal set of rules implicitly described by some dataset of training samples. As the number of samples and/or attributes in the dataset increases, the required construction time becomes the limiting factor for interactive or even functional use. The problem is emphasized if tree derivation is part of an iterative optimization method, such as boosting. Attempts to parallelize the construction of classification trees have therefore been presented in the past. This paper describes a parallel method for binary classification tree construction implemented on a graphics processing unit (GPU) using compute unified device architecture (CUDA). By employing node‐level, attribute‐level, and split‐level parallelism, the task parallel and data parallel sections of tree induction are mapped to the architecture of a modern GPU. The GPU‐based solution is compared with the sequential and multi‐threaded CPU versions on public access datasets, and it is shown that an order of magnitude acceleration can be achieved on this data‐intensive task using inexpensive commodity hardware. The influence of dataset characteristics on the efficiency of parallel implementation is also analyzed. Copyright © 2015 John Wiley &amp; Sons, Ltd.

GPU-OSDDA: a bit-vector GPU-based deadlock detection algorithm for single-unit resource systems

This article presents a GPU-based single-unit deadlock detection methodology and its algorithm, GPU-OSDDA. Our GPU-based design utilizes parallel hardware of GPU to perform computations and thus is able to overcome the major limitation of prior hardware-based approaches by having the capability of handling thousands of processes and resources, whilst achieving real-world run-times. By utilizing a bit-vector technique for storing algorithm matrices and designing novel, efficient algorithmic methods, we not only reduce memory usage dramatically but also achieve two orders of magnitude speedup over CPU equivalents. Additionally, GPU-OSDDA acts as an interactive service to the CPU, because all of the aforementioned computations and matrix management techniques take place on the GPU, requiring minimal interaction with the CPU. GPU-OSDDA is implemented on three GPU cards: Tesla C2050, Tesla K20c, and Titan X. Our design shows overall speedups of 6-595X over CPU equivalents.

Real-time dynamic programming for Markov decision processes with imprecise probabilities

Markov Decision Processes have become the standard model for probabilistic planning. However, when applied to many practical problems, the estimates of transition probabilities are inaccurate. This may be due to conflicting elicitations from experts or insufficient state transition information. The Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) was introduced to obtain a robust policy where there is uncertainty in the transition. Although it has been proposed a symbolic dynamic programming algorithm for MDP-IPs (called SPUDD-IP) that can solve problems up to 22 state variables, in practice, solving MDP-IP problems is time-consuming. In this paper we propose efficient algorithms for a more general class of MDP-IPs, called Stochastic Shortest Path MDP-IPs (SSP MDP-IPs) that use initial state information to solve complex problems by focusing on reachable states. The (L)RTDP-IP algorithm, a (Labeled) Real Time Dynamic Programming algorithm for SSP MDP-IPs, is proposed together with three different methods for sampling the next state. It is shown here that the convergence of (L)RTDP-IP can be obtained by using any of these three methods, although the Bellman backups for this class of problems prescribe a minimax optimization. As far as we are aware, this is the first asynchronous algorithm for SSP MDP-IPs given in terms of a general set of probability constraints that requires non-linear optimization over imprecise probabilities in the Bellman backup. Our results show up to three orders of magnitude speedup for (L)RTDP-IP when compared with the SPUDD-IP algorithm.

Accelerated Molecular Mechanical and Solvation Energetics on Multicore CPUs and Manycore GPUs.

Despite several reported acceleration successes of programmable GPUs (Graphics Processing Units) for molecular modeling and simulation tools, the general focus has been on fast computation with small molecules. This was primarily due to the limited memory size on the GPU. Moreover simultaneous use of CPU and GPU cores for a single kernel execution - a necessity for achieving high parallelism - has also not been fully considered. We present fast computation methods for molecular mechanical (Lennard-Jones and Coulombic) and generalized Born solvation energetics which run on commodity multicore CPUs and manycore GPUs. The key idea is to trade off accuracy of pairwise, long-range atomistic energetics for higher speed of execution. A simple yet efficient CUDA kernel for GPU acceleration is presented which ensures high arithmetic intensity and memory efficiency. Our CUDA kernel uses a cache-friendly, recursive and linear-space octree data structure to handle very large molecular structures with up to several million atoms. Based on this CUDA kernel, we present a hybrid method which simultaneously exploits both CPU and GPU cores to provide the best performance based on selected parameters of the approximation scheme. Our CUDA kernels achieve more than two orders of magnitude speedup over serial computation for many of the molecular energetics terms. The hybrid method is shown to be able to achieve the best performance for all values of the approximation parameter. The source code and binaries are freely available as PMEOPA (Parallel Molecular Energetic using Octree Pairwise Approximation) and downloadable from http://cvcweb.ices.utexas.edu/software.

All-Pairs Shortest Path algorithms for planar graph for GPU-accelerated clusters

We present a new approach for solving the All-Pairs Shortest-Path (APSP) problem for planar graphs that exploits the massive on-chip parallelism available in today’s Graphics Processing Units (GPUs). We describe two new algorithms based on our approach. Both algorithms use Floyd–Warshall method, have near optimal complexity in terms of the total number of operations, while their matrix-based structure is regular enough to allow for efficient parallel implementation on the GPUs. By applying a divide-and-conquer approach, we are able to make use of multi-node GPU clusters, resulting in more than an order of magnitude speedup over fastest known Dijkstra-based GPU implementation and a two-fold speedup over a parallel Dijkstra-based CPU implementation.

Analyzing competitive influence maximization problems with partial information: An approximation algorithmic framework

Given the popularity of the viral marketing campaign in online social networks, finding a computationally efficient method to identify a set of most influential nodes so as to compete well with others is of the utmost importance. In this paper, we propose a general model to describe the influence propagation of multiple competing sources in the same network. We formulate the Competitive Influence Maximization with Partial information (CIMP) problem: given an influence propagation model and the probability of a node being in the competitor’s seed set, how to find a set of k seeds so to trigger the largest expected influence cascade under the presence of other competitors? We propose a general algorithmic framework, Two-phase Competitive Influence Maximization (TCIM), to address the CIMP problem. TCIM returns a (1−1/e−ϵ)-approximate solution with probability of at least 1−n−ℓ, where ℓ≥1/2 is a parameter controlling the trade-off between the success probability and the computational efficiency. TCIM has an efficient expected time complexity of O(c(k+ℓ)(m+n)logn/ϵ2), where n and m are the number of nodes and edges in the network, and c is a function of the given propagation model (which may depend on k and the underlying network). To the best of our knowledge, this is the first work which provides a general framework for the competitive influence maximization problem where the seeds of the competitor could be given as an explicit set of seed nodes or a probability distribution of seed nodes. Moreover, our algorithmic framework provides both quality guarantee of solution and practical computational efficiency. We conduct extensive experiments on real-world datasets under three specific influence propagation models, and show the efficiency and accuracy of our framework. In particular, for the case where the seed set of the competitor is given explicitly, we achieve up to four orders of magnitude speedup as compared to previous algorithms with the same quality guarantee. When the competitor’s seed set is not given explicitly, running TCIM using the probability distribution of the competitor’s seeds returns nodes with higher expected influence than those nodes returned by TCIM using an explicit guess of the competitor’s seeds.