Parallel Graph Research Articles

A polynomial time algorithm to compute the connected treewidth of a series–parallel graph

It is well known that the treewidth of a graph G corresponds to the node search number where a team of searchers is pursuing a fugitive that is lazy and invisible (or alternatively is agile and visible) and has the ability to move with infinite speed via unguarded paths. Recently, monotone and connected node search strategies have been considered. A search strategy is monotone if it prevents the fugitive from pervading again areas from where he had been expelled and is connected if, at each step, the set of vertices that is or has been occupied by the searchers induces a connected subgraph of G. It has been shown that the corresponding connected and monotone search number of a graph G can be expressed as the connected treewidth, denoted by ctw(G), that is defined as the minimum width of a rooted tree-decomposition (X,T,r), where the union of the bags corresponding to the nodes of a path of T containing the root r is connected in G. In this paper, we initiate the algorithmic study of connected treewidth. We design a O(n2⋅logn)-time dynamic programming algorithm to compute the connected treewidth of biconnected series–parallel graphs. At the price of an extra n factor in the running time, our algorithm generalizes to graphs of treewidth at most two.

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the interfaces, optimizations, and graph processing techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph Based Benchmark Suite (GBBS).

Distributed and incremental travelling salesman algorithm on time-evolving graphs

Travelling salesman problem (TSP) is a graph problem that has been widely used in many applications, especially for transportation and logistics. Because TSP is a NP hard problem, minimizing the complexity of TSP algorithms is an important problem. Many heuristic algorithms have been proposed to compute the TSP tours of a given static graph. But limited studies have been done on time-evolving graph (TEG) where the graph can change over time due to update events, such as weight changes on edges or vertices. It is a more challenging problem because the speed of TSP computations must be high enough to catch up the graph update frequency. In this paper, we make the very first attempt to minimize the computation time of solving TSP on time-evolving graphs. By exploring parallel computing power and reusing previous computing results, we proposed a distributed and incremental TSP algorithm which can be implemented on vertex-centric parallel graph computing frameworks to efficiently find TSP tours on large changing graphs. Our incremental algorithm can maintain shortest TSP tour with minimum amount of recomputation. Through our experimental evaluation, we have shown incremental TSP algorithm is 98% faster than distributed algorithm.

A Parallel Meta-Heuristic Approach to Reduce Vehicle Travel Time in Smart Cities

The development of the smart city concept and inhabitants’ need to reduce travel time, in addition to society’s awareness of the importance of reducing fuel consumption and respecting the environment, have led to a new approach to the classic travelling salesman problem (TSP) applied to urban environments. This problem can be formulated as “Given a list of geographic points and the distances between each pair of points, what is the shortest possible route that visits each point and returns to the departure point?”. At present, with the development of Internet of Things (IoT) devices and increased capabilities of sensors, a large amount of data and measurements are available, allowing researchers to model accurately the routes to choose. In this work, the aim is to provide a solution to the TSP in smart city environments using a modified version of the metaheuristic optimization algorithm Teacher Learner Based Optimization (TLBO). In addition, to improve performance, the solution is implemented by means of a parallel graphics processing unit (GPU) architecture, specifically a Compute Unified Device Architecture (CUDA) implementation.

GPU-oriented dynamic low-power data transmission method

The model highly parallel graphics processor systems rely on high-bandwidth DRAM I/O interfaces for large volume of data access at the cost of a lot of energy consumption. In order to reduce the energy consumption of data transmission, modern DRAM uses an asymmetric pseudo-drain I/O interface, which increases the ratio of the termination energy to the transmission energy of logic value 1 in data transactions. This paper proposes the X + B Dynamic Bus Encoding Mechanism, which dynamically selects the encoding mechanism to reduce the number of logical values 1 within different data elements, thereby reducing the data transmission energy consumption of the modern DRAM data bus. The simulation evaluation shows the X + B Dynamic Bus Encoding Mechanism reduces the number of logical values 1 by 38.6%, which saves 31.4% of transmission energy consumption compared to the current bus coding technology.

SRGAT: Single Image Super-Resolution With Graph Attention Network

Deep neural networks have demonstrated remarkable reconstruction for single-image super-resolution (SISR). However, most existing CNN-based SISR methods directly learn the relation between low-resolution (LR) and high-resolution (HR) images, neglecting to explore the recurrence of internal patches, hence hindering the representational power of CNNs. In this paper, we propose a novel single image Super-Resolution network based on Graph ATtention network (SRGAT) to make full use of the internal patch-recurrence in a natural image. The proposed model employs a feature mapping block with a recurrent structure to refine low-level representations with high-level information. Especifically, the feature mapping block contains a parallel graph similarity branch and a content branch, where the graph similarity branch aims at exploiting the similarity and symmetry across different image patches in low-resolution feature space and provides additional priors for the content branch to enhance texture details. Specifically, we consider the internal patch-recurrence of an image by constructing a graph network on image feature patches. In this way, the information from neighboring patches can be interacted using graph attention network (GAT) to help it recover additional textures, which complements the textures learned from the content branch. Extensive quantitative and qualitative evaluations on five benchmark datasets demonstrate that the proposed algorithm performs favorably against the state-of-the-art super-resolution methods.

Feluca: A Two-Stage Graph Coloring Algorithm With Color-Centric Paradigm on GPU

There are great challenges in performing graph coloring on GPU in general. First, the long-tail problem exists in the recursion algorithm because the conflict (i.e., different threads assign the adjacent nodes to the same color) becomes more likely to occur as the number of iterations increases. Second, it is hard to parallelize the sequential spread algorithm because the color allocation depends on the adjoining iteration. Third, the atomic operation is widely used on GPU to maintain the color list, which can greatly reduce the efficiency of GPU threads. In this article, we propose a two-stage high-performance graph coloring algorithm, called Feluca, aiming to address the above challenges. Feluca combines the recursion-based method with the sequential spread-based method. In the first stage, Feluca uses a recursive routine to color a majority of vertices in the graph. Then, it switches to the sequential spread method to color the remaining vertices in order to avoid the conflicts of the recursive algorithm. Moreover, the following techniques are proposed to further improve the graph coloring performance. i) A new method is proposed to eliminate the cycles in the graph; ii) a top-down scheme is developed to avoid the atomic operation originally required for color selection; and iii) a novel color-centric coloring paradigm is designed to improve the degree of parallelism for the sequential spread part. All these newly developed techniques, together with further GPU-specific optimizations such as coalesced memory access, comprise an efficient parallel graph coloring solution in Feluca. We have conducted extensive experiments on NVIDIA GPU. The results show that Feluca can achieve 1.19 - 8.39× speedup over the state-of-the-art algorithms.

A Case Study on Generative Building Skin Forming by Employing Building Information Modelling (BIM) Tools

Purpose This study aims to produce generative curtain wall geometries based on predetermined parameters such as storey information, shadow zones, preliminary building unit cost, frequency, etc. in a BIM platform for the preliminary design of a future project in Basmane and understand its novel outcomes and implications.Design/Methodology/Approach The methodology is construed over four successive phases, namely: the built environment modeling, analyses for a solid understanding of the study area, determination of the generative design criteria, and finally design solutions. In the initial phase, the case-study building in Basmane with the surrounding environment was digitally modeled for the following analyses. Several programs apart from BIM have been utilized for the daylight zones and wind simulations. The daylight areas affecting the surface of the studied building were marked schematically per the simulation data. Subsequently, the area of the curtain wall, material type, preliminary building unit cost (assembly/labor and material cost), the height of storey, the density of elements, and fixed shading devices parameters were tested via optimization thru generative design methodology and provide potential design solutions by utilization of BIM tools.Findings The findings of this study could be boiled down to a single comprehensive objective of generating outputs of assorted design solutions thru a generative design approach. When the output data set is visualized via parallel coordinate graphs, it could be well articulated that the classification of rule-based relationships and the criteria interrelations were based on the designer's decisions.Research Limitations/Implications This study was examined on a case basis by an experimental approach. It shall be considered that the curtain wall construction encompasses diverse materials, connection details, and construction techniques that affect the final cost thus this research was conducted at the preliminary design stage and might not reflect actual costs.Social/Practical Implications Albeit the technical aspect of the curtain walls is not included in this case study, it helps generative design culture by demonstrating the extent of the opportunities it offers to designers in the preliminary design stage.Originality/Value This study is a show-case of a preliminary design for an actual building stock in the vicinity of Basmane focusing on the building envelope design process with multiple parameters and should be regarded as an opportunity to understand how innovative solutions alike are put forward for the use of designers.

Effect of Al Concentration on the Microstructural Evolution of Fe-Cr-Al Systems: A Phase-Field Approach

In this study, the microstructural evolution of an Fe-Cr-Al system was simulated in two-dimensional (2D) and three-dimensional (3D) systems using the phase-field method. We investigated the effect of Al concentration on the microstructural evolution of the systems, with a focus on the nucleation and growth of the Cr-rich α′ phase. In addition, we quantitatively analyzed the mechanism of the effect of Al concentration on the microstructural characteristics of the 2D and 3D systems, such as the number of precipitates, average precipitate area (volume), and α′ phase fraction. In particular, we analyzed the effect of Al concentration and the dimensions of the system cell on the formation of the interconnected structure at high Cr concentrations, such as 35 Crat% and 40 Crat%. To enhance the performance of the simulations, we applied a semi-implicit Fourier spectral method for the ternary system and a parallel graphics processing unit computing technique. The results revealed that the initiation of phase separation in the 2D and 3D simulations was enhanced with an increase in the average Al concentration in the system. In addition, with an increase in the average Al concentration in both systems, the α′ phase fraction increased, while the change in the phase fraction decreased.

A comparison of different metaheuristics for the quadratic assignment problem in accelerated systems

Although metaheuristics are used for solving complex and real-world problems, they do not provide an exact solution, but only an approximate solution in feasible time. However, for very large instances, a metaheuristic may take a considerable amount of time. Therefore, we utilize a highly parallel metaheuristic to run on a modern massively parallel graphics processing unit (GPU) to further reduce the execution time. Additionally, because metaheuristics are not problem-specific, it is interesting to determine which metaheuristic is best for each problem type. In this study, using a massive parallel machine such as a GPU, we evaluate the performance of different metaheuristics such as the iterated local search, simulated annealing, genetic algorithm, tabu search, particle swarm optimization, and crow search algorithm with respect to the quadratic assignment problem.

High-Quality Shared-Memory Graph Partitioning

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically. Unfortunately, previous approaches to parallel graph partitioning have problems in this context since they often show a negative trade-off between speed and quality. We present an approach to multi-level shared-memory parallel graph partitioning that produces balanced solutions, shows high speedups for a variety of large graphs and yields very good quality independently of the number of cores used. For example, in an extensive experimental study, at 79 cores, one of our closest competitors is faster but fails to meet the balance criterion in the majority of cases and another is mostly slower and incurs about 13 percent larger cut size. Important ingredients include parallel label propagation for both coarsening and refinement, parallel initial partitioning, a simple yet effective approach to parallel localized local search, and fast locality preserving hash tables.

Visual Simultaneous Localization and Mapping with Applications to Monitoring of Underground Transportation Infrastructure

This paper presents the results of the development, design, and implementation of a visual simultaneous localization and mapping (SLAM) system for autonomous real-time localization with application to underground transportation infrastructure (UTI) such as tunnels. Localization is achieved in the absence of any global positioning system (GPS) or auxiliary system. The indoor localization system is a necessary element of a fully autonomous platform for the detection of cracks and other anomalies on the interior surfaces of tunnels and other UTI. It can be used for tagging of high-resolution sensor data obtained with low-cost prototype data acquisition platforms previously developed. Visual based SLAM has been used as the core element in an architecture employing a commercial off-the-shelf (COTS) ZED stereo camera from Stereolabs. To achieve real-time operation, an NVIDIA Jetson TX2 massively parallel graphics processing unit (GPU) was used as the core computational engine employing two different software libraries. We achieved localization at 5 frames per second (FPS) using ORBSLAM2 open-source software library, and the much lighter, but proprietary, ZED SDK was able to deliver a performance at nearly 60 FPS. To assess the accuracy of the relative localization system, we conducted several tests at 30 FPS and reported on the resulting error variances that were found to be consistently very small. Finally, we conducted several tests in a tunnel in the Los Angeles county area and confirmed the applicability of the method for monitoring UTI.

Pyntacle: a parallel computing-enabled framework for large-scale network biology analysis.

BackgroundSome natural systems are big in size, complex, and often characterized by convoluted mechanisms of interaction, such as epistasis, pleiotropy, and trophism, which cannot be immediately ascribed to individual natural events or biological entities but that are often derived from group effects. However, the determination of important groups of entities, such as genes or proteins, in complex systems is considered a computationally hard task.ResultsWe present Pyntacle, a high-performance framework designed to exploit parallel computing and graph theory to efficiently identify critical groups in big networks and in scenarios that cannot be tackled with traditional network analysis approaches.ConclusionsWe showcase potential applications of Pyntacle with transcriptomics and structural biology data, thereby highlighting the outstanding improvement in terms of computational resources over existing tools.

Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs

In this work, we solve the problem of the coexistence of periodic orbits in homogeneous Boolean graph dynamical systems that are induced by a maxterm or a minterm (Boolean) function, with a direct underlying dependency graph. Specifically, we show that periodic orbits of any period can coexist in both kinds of update schedules, parallel and sequential. This result contrasts with the properties of their counterparts over undirected graphs with the same evolution operators, where fixed points cannot coexist with periodic orbits of other different periods. These results complete the study of the periodic structure of homogeneous Boolean graph dynamical systems on maxterm and minterm functions.

Distributed Application Global States Monitoring in PEGASUS DA Applied to Parallel Graph Partitioning

SummaryThis paper presents how parallel advanced graph partitioning algorithms can be designed and improved with the use of global application states monitoring of distributed programs. The proposed algorithms have been implemented inside a novel distributed program design framework Program Execution Governed by Asynchronous Supervision of States in Distributed Applications (PEGASUS DA). This framework provides system support for the design of execution control in distributed applications based on automated global state monitoring. Two strategies for the control design of advanced parallel/distributed graph partitioning algorithms are presented and discussed. In the first one, the parallel algorithm control runs on top of the popular graph partitioning METIS tool. The second control strategy is based on genetic programming so that partitioning primitives and the overall algorithmic control can be freely designed by the user. Advanced partitioning methods have been conveniently embedded inside the global state monitoring driven PEGASUS DA framework which controls partitioning distributed actions at the level of processes and threads. The use of the framework allowed easy design and testing of different graph optimization strategies. The presented graph partitioning methods are illustrated by experiments with benchmark graphs. The experiments have comparatively assessed the obtained graph partitioning quality (visible improvement has been observed) and have identified benefits of the proposed approach for programmers.

An Efficient Data Retrieval Parallel Reeb Graph Algorithm

The Reeb graph of a scalar function that is defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence, the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms.

Counting Periodic Points in Parallel Graph Dynamical Systems

Let F:0,1n⟶0,1n be a parallel dynamical system over an undirected graph with a Boolean maxterm or minterm function as a global evolution operator. It is well known that every periodic point has at most two periods. Actually, periodic points of different periods cannot coexist, and a fixed point theorem is also known. In addition, an upper bound for the number of periodic points of F has been given. In this paper, we complete the study, solving the minimum number of periodic points’ problem for this kind of dynamical systems which has been usually considered from the point of view of complexity. In order to do this, we use methods based on the notions of minimal dominating sets and maximal independent sets in graphs, respectively. More specifically, we find a lower bound for the number of fixed points and a lower bound for the number of 2-periodic points of F. In addition, we provide a formula that allows us to calculate the exact number of fixed points. Furthermore, we provide some conditions under which these lower bounds are attained, thus generalizing the fixed-point theorem and the 2-period theorem for these systems.

Fast shared-memory streaming multilevel graph partitioning

A fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.

Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling.

This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave-structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.

Parallel graph algorithms in constant adaptive rounds

We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only O ( n ϵ ) space per machine, where 0 < ϵ < 1. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distributed computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines.