Task-based Augmented Contour Trees with Fibonacci Heaps

This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of contour tree based applications including data segmentation. Our approach completely revisits the traditional, sequential contour tree algorithm to re-formulate all the steps of the computation as a set of independent local tasks. This includes a new computation procedure based on Fibonacci heaps for the join and split trees, two intermediate data structures used to compute the contour tree, whose constructions are efficiently carried out concurrently thanks to the dynamic scheduling of task parallelism. We also introduce a new parallel algorithm for the combination of these two trees into the output global contour tree. Overall, this results in superior time performance in practice, both in sequential and in parallel thanks to the OpenMP task runtime. We report performance numbers that compare our approach to reference sequential and multi-threaded implementations for the computation of augmented merge and contour trees. These experiments demonstrate the run-time efficiency of our approach and its scalability on common workstations. We demonstrate the utility of our approach in data segmentation applications

Gunrock: GPU Graph Analytics

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused 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 characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU

Performance Characterization of Multi-threaded Graph Processing Applications on Intel Many-Integrated-Core Architecture

Intel Xeon Phi many-integrated-core (MIC) architectures usher in a new era of terascale integration. Among emerging killer applications, parallel graph processing has been a critical technique to analyze connected data. In this paper, we empirically evaluate various computing platforms including an Intel Xeon E5 CPU, a Nvidia Geforce GTX1070 GPU and an Xeon Phi 7210 processor codenamed Knights Landing (KNL) in the domain of parallel graph processing. We show that the KNL gains encouraging performance when processing graphs, so that it can become a promising solution to accelerating multi-threaded graph applications. We further characterize the impact of KNL architectural enhancements on the performance of a state-of-the art graph framework.We have four key observations: 1 Different graph applications require distinctive numbers of threads to reach the peak performance. For the same application, various datasets need even different numbers of threads to achieve the best performance. 2 Only a few graph applications benefit from the high bandwidth MCDRAM, while others favor the low latency DDR4 DRAM. 3 Vector processing units executing AVX512 SIMD instructions on KNLs are underutilized when running the state-of-the-art graph framework. 4 The sub-NUMA cache clustering mode offering the lowest local memory access latency hurts the performance of graph benchmarks that are lack of NUMA awareness. At last, We suggest future works including system auto-tuning tools and graph framework optimizations to fully exploit the potential of KNL for parallel graph processing.Comment: published as L. Jiang, L. Chen and J. Qiu, "Performance Characterization of Multi-threaded Graph Processing Applications on Many-Integrated-Core Architecture," 2018 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS), Belfast, United Kingdom, 2018, pp. 199-20

Finding Hexahedrizations for Small Quadrangulations of the Sphere

This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is the first practical solution to the problem. It is able to compute small hexahedral meshes of quadrangulations for which the previously known best solutions could only be built by hand or contained thousands of hexahedra. These challenging quadrangulations include the boundaries of transition templates that are critical for the success of general hexahedral meshing algorithms. The algorithm proposed in this paper is dedicated to building combinatorial hexahedral meshes of small quadrangulations and ignores the geometrical problem. The key idea of the method is to exploit the equivalence between quad flips in the boundary and the insertion of hexahedra glued to this boundary. The tree of all sequences of flipping operations is explored, searching for a path that transforms the input quadrangulation Q into a new quadrangulation for which a hexahedral mesh is known. When a small hexahedral mesh exists, a sequence transforming Q into the boundary of a cube is found; otherwise, a set of pre-computed hexahedral meshes is used. A novel approach to deal with the large number of problem symmetries is proposed. Combined with an efficient backtracking search, it allows small shellable hexahedral meshes to be found for all even quadrangulations with up to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more than 72 hexahedra. This algorithm is also used to find a construction to fill arbitrary domains, thereby proving that any ball-shaped domain bounded by n quadrangles can be meshed with no more than 78 n hexahedra. This very significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201

Distributed-Memory Breadth-First Search on Massive Graphs

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451