Fast and high quality topology-aware task mapping

Considering the large number of processors and the size of the interconnection networks on exascale capable supercomputers, mapping concurrently executable and communicating tasks of an application is a complex problem that needs to be dealt with care. For parallel applications, the communication overhead can be a significant bottleneck on scalability. Topology-aware task-mapping methods that map the tasks to the processors (i.e., cores) by exploiting the underlying network information are very effective to avoid, or at worst bend, this limitation. We propose novel, efficient, and effective task mapping algorithms employing a graph model. The experiments show that the methods are faster than the existing approaches proposed for the same task, and on 4096 processors, the algorithms improve the communication hops and link contentions by 16% and 32%, respectively, on the average. In addition, they improve the average execution time of a parallel SpMV kernel and a communication-only application by 9% and 14%, respectively

Meerkat: A framework for Dynamic Graph Algorithms on GPUs

Graph algorithms are challenging to implement due to their varying topology and irregular access patterns. Real-world graphs are dynamic in nature and routinely undergo edge and vertex additions, as well as, deletions. Typical examples of dynamic graphs are social networks, collaboration networks, and road networks. Applying static algorithms repeatedly on dynamic graphs is inefficient. Unfortunately, we know little about how to efficiently process dynamic graphs on massively parallel architectures such as GPUs. Existing approaches to represent and process dynamic graphs are either not general or inefficient. In this work, we propose a library-based framework for dynamic graph algorithms that proposes a GPU-tailored graph representation and exploits the warp-cooperative execution model. The library, named Meerkat, builds upon a recently proposed dynamic graph representation on GPUs. This representation exploits a hashtable-based mechanism to store a vertex's neighborhood. Meerkat also enables fast iteration through a group of vertices, such as the whole set of vertices or the neighbors of a vertex. Based on the efficient iterative patterns encoded in Meerkat, we implement dynamic versions of the popular graph algorithms such as breadth-first search, single-source shortest paths, triangle counting, weakly connected components, and PageRank. Compared to the state-of-the-art dynamic graph analytics framework Hornet, Meerkat is $12.6\times$, $12.94\times$, and $6.1\times$ faster, for query, insert, and delete operations, respectively. Using a variety of real-world graphs, we observe that Meerkat significantly improves the efficiency of the underlying dynamic graph algorithm. Meerkat performs $1.17\times$ for BFS, $1.32\times$ for SSSP, $1.74\times$ for PageRank, and $6.08\times$ for WCC, better than Hornet on average

Fast and high quality topology-aware task mapping

International audienceConsidering the large number of processors and the size of the interconnection networks on exascale-capable supercomputers, mapping concurrently executable and communicating tasks of an application is a complex problem that needs to be dealt with care. For parallel applications, the communication overhead can be a significant bottleneck on scalability. Topology-aware task-mapping methods that map the tasks to the processors (i.e., cores) by exploiting the underlying network information are very effective to avoid, or at worst bend, this limitation. We propose novel, efficient, and effective task mapping algorithms employing a graph model. The experiments show that the methods are faster than the existing approaches proposed for the same task, and on 4096 processors, the algorithms improve the communication hops and link contentions by 16% and 32%, respectively, on the average. In addition, they improve the average execution time of a parallel SpMV kernel and a communication-only application by 9% and 14%, respectively

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

Practical Minimum Cut Algorithms

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability

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