Time and Memory Efficient Parallel Algorithm for Structural Graph Summaries and two Extensions to Incremental Summarization and kk-Bisimulation for Long kk-Chaining

We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal language. An extension of the parallel base algorithm allows incremental graph summarization. In this paper, we prove that the incremental algorithm is correct and show that updates are performed in time $\mathcal{O}(\Delta \cdot d^k)$, where $\Delta$ is the number of additions, deletions, and modifications to the input graph, $d$ the maximum degree, and $k$ is the maximum distance in the subgraphs considered. Although the iterative algorithm supports values of $k>1$, it requires nested data structures for the message passing that are memory-inefficient. Thus, we extended the base summarization algorithm by a hash-based messaging mechanism to support a scalable iterative computation of graph summarizations based on $k$-bisimulation for arbitrary $k$. We empirically evaluate the performance of our algorithms using benchmark and real-world datasets. The incremental algorithm almost always outperforms the batch computation. We observe in our experiments that the incremental algorithm is faster even in cases when $50\%$ of the graph database changes from one version to the next. The incremental computation requires a three-layered hash index, which has a low memory overhead of only $8\%$ ($\pm 1\%$). Finally, the incremental summarization algorithm outperforms the batch algorithm even with fewer cores. The iterative parallel $k$-bisimulation algorithm computes summaries on graphs with over $10$M edges within seconds. We show that the algorithm processes graphs of $100+\,$M edges within a few minutes while having a moderate memory consumption of $<150$ GB. For the largest BSBM1B dataset with 1 billion edges, it computes $k=10$ bisimulation in under an hour

Multi-Head Graph Convolutional Network for Structural Connectome Classification

We tackle classification based on brain connectivity derived from diffusion magnetic resonance images. We propose a machine-learning model inspired by graph convolutional networks (GCNs), which takes a brain connectivity input graph and processes the data separately through a parallel GCN mechanism with multiple heads. The proposed network is a simple design that employs different heads involving graph convolutions focused on edges and nodes, capturing representations from the input data thoroughly. To test the ability of our model to extract complementary and representative features from brain connectivity data, we chose the task of sex classification. This quantifies the degree to which the connectome varies depending on the sex, which is important for improving our understanding of health and disease in both sexes. We show experiments on two publicly available datasets: PREVENT-AD (347 subjects) and OASIS3 (771 subjects). The proposed model demonstrates the highest performance compared to the existing machine-learning algorithms we tested, including classical methods and (graph and non-graph) deep learning. We provide a detailed analysis of each component of our model

Research on High-performance and Scalable Data Access in Parallel Big Data Computing

To facilitate big data processing, many dedicated data-intensive storage systems such as Google File System(GFS), Hadoop Distributed File System(HDFS) and Quantcast File System(QFS) have been developed. Currently, the Hadoop Distributed File System(HDFS) [20] is the state-of-art and most popular open-source distributed file system for big data processing. It is widely deployed as the bedrock for many big data processing systems/frameworks, such as the script-based pig system, MPI-based parallel programs, graph processing systems and scala/java-based Spark frameworks. These systems/applications employ parallel processes/executors to speed up data processing within scale-out clusters. Job or task schedulers in parallel big data applications such as mpiBLAST and ParaView can maximize the usage of computing resources such as memory and CPU by tracking resource consumption/availability for task assignment. However, since these schedulers do not take the distributed I/O resources and global data distribution into consideration, the data requests from parallel processes/executors in big data processing will unfortunately be served in an imbalanced fashion on the distributed storage servers. These imbalanced access patterns among storage nodes are caused because a). unlike conventional parallel file system using striping policies to evenly distribute data among storage nodes, data-intensive file systems such as HDFS store each data unit, referred to as chunk or block file, with several copies based on a relative random policy, which can result in an uneven data distribution among storage nodes; b). based on the data retrieval policy in HDFS, the more data a storage node contains, the higher the probability that the storage node could be selected to serve the data. Therefore, on the nodes serving multiple chunk files, the data requests from different processes/executors will compete for shared resources such as hard disk head and network bandwidth. Because of this, the makespan of the entire program could be significantly prolonged and the overall I/O performance will degrade. The first part of my dissertation seeks to address aspects of these problems by creating an I/O middleware system and designing matching-based algorithms to optimize data access in parallel big data processing. To address the problem of remote data movement, we develop an I/O middleware system, called SLAM, which allows MPI-based analysis and visualization programs to benefit from locality read, i.e, each MPI process can access its required data from a local or nearby storage node. This can greatly improve the execution performance by reducing the amount of data movement over network. Furthermore, to address the problem of imbalanced data access, we propose a method called Opass, which models the data read requests that are issued by parallel applications to cluster nodes as a graph data structure where edges weights encode the demands of load capacity. We then employ matching-based algorithms to map processes to data to achieve data access in a balanced fashion. The final part of my dissertation focuses on optimizing sub-dataset analyses in parallel big data processing. Our proposed methods can benefit different analysis applications with various computational requirements and the experiments on different cluster testbeds show their applicability and scalability

PT-Scotch: A tool for efficient parallel graph ordering

The parallel ordering of large graphs is a difficult problem, because on the one hand minimum degree algorithms do not parallelize well, and on the other hand the obtainment of high quality orderings with the nested dissection algorithm requires efficient graph bipartitioning heuristics, the best sequential implementations of which are also hard to parallelize. This paper presents a set of algorithms, implemented in the PT-Scotch software package, which allows one to order large graphs in parallel, yielding orderings the quality of which is only slightly worse than the one of state-of-the-art sequential algorithms. Our implementation uses the classical nested dissection approach but relies on several novel features to solve the parallel graph bipartitioning problem. Thanks to these improvements, PT-Scotch produces consistently better orderings than ParMeTiS on large numbers of processors

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulation that also exploits multiple (intra-node and inter-node) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research

Parallel ACO with a Ring Neighborhood for Dynamic TSP

The current paper introduces a new parallel computing technique based on ant colony optimization for a dynamic routing problem. In the dynamic traveling salesman problem the distances between cities as travel times are no longer fixed. The new technique uses a parallel model for a problem variant that allows a slight movement of nodes within their Neighborhoods. The algorithm is tested with success on several large data sets.Comment: 8 pages, 1 figure; accepted J. Information Technology Researc