Platform Dependent Verification: On Engineering Verification Tools for 21st Century

The paper overviews recent developments in platform-dependent explicit-state LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006

Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop on the Applications of Matrix Computational Methods in the Analysis of Modern Dat

Breadth First Search Vectorization on the Intel Xeon Phi

Breadth First Search (BFS) is a building block for graph algorithms and has recently been used for large scale analysis of information in a variety of applications including social networks, graph databases and web searching. Due to its importance, a number of different parallel programming models and architectures have been exploited to optimize the BFS. However, due to the irregular memory access patterns and the unstructured nature of the large graphs, its efficient parallelization is a challenge. The Xeon Phi is a massively parallel architecture available as an off-the-shelf accelerator, which includes a powerful 512 bit vector unit with optimized scatter and gather functions. Given its potential benefits, work related to graph traversing on this architecture is an active area of research. We present a set of experiments in which we explore architectural features of the Xeon Phi and how best to exploit them in a top-down BFS algorithm but the techniques can be applied to the current state-of-the-art hybrid, top-down plus bottom-up, algorithms. We focus on the exploitation of the vector unit by developing an improved highly vectorized OpenMP parallel algorithm, using vector intrinsics, and understanding the use of data alignment and prefetching. In addition, we investigate the impact of hyperthreading and thread affinity on performance, a topic that appears under researched in the literature. As a result, we achieve what we believe is the fastest published top-down BFS algorithm on the version of Xeon Phi used in our experiments. The vectorized BFS top-down source code presented in this paper can be available on request as free-to-use software

Evaluation of vectorization potential of Graph500 on Intel's Xeon Phi

Graph500 is a data intensive application for high performance computing and it is an increasingly important workload because graphs are a core part of most analytic applications. So far there is no work that examines if Graph500 is suitable for vectorization mostly due a lack of vector memory instructions for irregular memory accesses. The Xeon Phi is a massively parallel processor recently released by Intel with new features such as a wide 512-bit vector unit and vector scatter/gather instructions. Thus, the Xeon Phi allows for more efficient parallelization of Graph500 that is combined with vectorization. In this paper we vectorize Graph500 and analyze the impact of vectorization and prefetching on the Xeon Phi. We also show that the combination of parallelization, vectorization and prefetching yields a speedup of 27% over a parallel version with prefetching that does not leverage the vector capabilities of the Xeon Phi.The research leading to these results has received funding from the European Research Council under the European Unions 7th FP (FP/2007- 2013) / ERC GA n. 321253. It has been partially funded by the Spanish Government (TIN2012-34557)Peer ReviewedPostprint (published version

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