ST-connectivity poses a decision problem, determining whether, for vertices s and t within a graph, t is reachable from s . The challenge arises in the context of dynamic real-world graphs that undergo rapid evolution over time. In these scenarios, repeatedly solving the s-t connectivity problem from the beginning after each graph modification becomes impractical. Although parallel solutions, especially designed for GPUs, have been introduced to tackle the size complexity of static graphs, none have specifically addressed the concern of work efficiency in dynamic graphs. We propose an efficient solution for GPUs to the st-connectivity problem that can handle concurrent processing of batches of graph updates. We use batch information strategically to reduce the overall workload needed for updating the connectivity result. We provide experimental results based on standard datasets and with graphs of different characteristics and batch sizes to evaluate the proposed solutions efficiency. • The article presents an STCON solution for GPU architectures. • The solution targets dynamic graphs. • It shows the speedup and improvements wrt the static solution. • The results have been conducted on two large and standard datasets.

Likely invariants model properties that hold in operating conditions of a computing system. Dynamic mining of invariants aims at extracting logic formulas representing such properties from the system execution traces, and it is widely used for verification of intellectual property (IP) blocks. Although the extracted formulas represent likely invariants that hold in the considered traces, there is no guarantee that they are true in general for the system under verification. As a consequence, to increase the probability that the mined invariants are true in general, dynamic mining has to be performed to large sets of representative execution traces. This makes the execution-based mining process of actual IP blocks very time-consuming due to the trace lengths and to the large sets of monitored signals. This article presents Mangrove, an efficient implementation of a dynamic invariant mining algorithm for GPU architectures. Mangrove exploits inference rules, which are applied at run time to filter invariants from the execution traces and, thus, to sensibly reduce the problem complexity. Mangrove allows users to define invariant templates and, from these templates, it automatically generates kernels for parallel and efficient mining on GPU architectures. The article presents the tool, the analysis of its performance, and its comparison with the best sequential and parallel implementations at the state of the art.

BACKGROUND: R has become the de-facto reference analysis environment in Bioinformatics. Plenty of tools are available as packages that extend the R functionality, and many of them target the analysis of biological networks. Several algorithms for graphs, which are the most adopted mathematical representation of networks, are well-known examples of applications that require high-performance computing, and for which classic sequential implementations are becoming inappropriate. In this context, parallel approaches targeting GPU architectures are becoming pervasive to deal with the execution time constraints. Although R packages for parallel execution on GPUs are already available, none of them provides graph algorithms. RESULTS: This work presents cuRnet, a R package that provides a parallel implementation for GPUs of the breath-first search (BFS), the single-source shortest paths (SSSP), and the strongly connected components (SCC) algorithms. The package allows offloading computing intensive applications to GPU devices for massively parallel computation and to speed up the runtime up to one order of magnitude with respect to the standard sequential computations on CPU. We have tested cuRnet on a benchmark of large protein interaction networks and for the interpretation of high-throughput omics data thought network analysis. CONCLUSIONS: cuRnet is a R package to speed up graph traversal and analysis through parallel computation on GPUs. We show the efficiency of cuRnet applied both to biological network analysis, which requires basic graph algorithms, and to complex existing procedures built upon such algorithms.

After publication of this supplement article [1], it was brought to our attention that reference 10 and reference 12 in the article are incorrect.

Tuning GPU applications is a very challenging task as any source-code optimization can sensibly impact performance, power, and energy consumption of the GPU device. Such an impact also depends on the GPU on which the application is run. This paper presents a suite of microbenchmarks that provides the actual characteristics of specific GPU device components (e.g., arithmetic instruction units, memories, etc.) in terms of throughput, power, and energy consumption. It shows how the suite can be combined to standard profiler information to efficiently drive the application tuning by considering the three design constraints (power, performance, energy consumption) and the characteristics of the target GPU device.

Workload partitioning and the subsequent work item-to-thread mapping are key aspects to face when implementing any efficient GPU application. Different techniques have been proposed to deal with such issues, ranging from the computationally simplest static to the most complex dynamic ones. Each of them finds the best use depending on the workload characteristics (static for more regular workloads, dynamic for irregular workloads). Nevertheless, no one of them provides a sound tradeoff when applied in both cases. Static approaches lead to load unbalancing with irregular problems, while the computational overhead introduced by the dynamic or semi-dynamic approaches often worsens the overall application performance when run on regular problems. This article presents an efficient dynamic technique for workload partitioning and work item-to-thread mapping whose complexity is significantly reduced with respect to the other dynamic approaches in literature. The article shows how the partitioning and mapping algorithm has been implemented by fully taking advantage of the GPU device characteristics with the aim of minimizing the involved computational overhead. The article shows, compares, and analyses the experimental results obtained by applying the proposed approach and several static, dynamic, and semi-dynamic techniques at the state of the art to different benchmarks and over different GPU technologies (i.e., NVIDIA Fermi, Kepler, and Maxwell) to understand when and how each technique best applies.

MOTIVATION: Biological network querying is a problem requiring a considerable computational effort to be solved. Given a target and a query network, it aims to find occurrences of the query in the target by considering topological and node similarities (i.e. mismatches between nodes, edges, or node labels). Querying tools that deal with similarities are crucial in biological network analysis because they provide meaningful results also in case of noisy data. In addition, as the size of available networks increases steadily, existing algorithms and tools are becoming unsuitable. This is rising new challenges for the design of more efficient and accurate solutions. RESULTS: This paper presents APPAGATO, a stochastic and parallel algorithm to find approximate occurrences of a query network in biological networks. APPAGATO handles node, edge and node label mismatches. Thanks to its randomic and parallel nature, it applies to large networks and, compared with existing tools, it provides higher performance as well as statistically significant more accurate results. Tests have been performed on protein-protein interaction networks annotated with synthetic and real gene ontology terms. Case studies have been done by querying protein complexes among different species and tissues. AVAILABILITY AND IMPLEMENTATION: APPAGATO has been developed on top of CUDA-C ++ Toolkit 7.0 framework. The software is available online http://profs.sci.univr.it/∼bombieri/APPAGATO CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Finding the shortest paths from a single source to all other vertices is a common problem in graph analysis. The Bellman-Ford's algorithm is the solution that solves such a single-source shortest path (SSSP) problem and better applies to be parallelized for many-core architectures. Nevertheless, the high degree of parallelism is guaranteed at the cost of low work efficiency, which, compared to similar algorithms in literature (e.g., Dijkstra's) involves much more redundant work and a consequent waste of power consumption. This article presents a parallel implementation of the Bellman-Ford algorithm that exploits the architectural characteristics of recent GPU architectures (i.e., NVIDIA Kepler, Maxwell) to improve both performance and work efficiency. The article presents different optimizations to the implementation, which are oriented both to the algorithm and to the architecture. The experimental results show that the proposed implementation provides an average speedup of$5 \times$higher than the existing most efficient parallel implementations for SSSP, that it works on graphs where those implementations cannot work or are inefficient (e.g., graphs with negative weight edges, sparse graphs), and that it sensibly reduces the redundant work caused by the parallelization process.

Dynamic mining of invariants is a class of approaches to extract logic formulas from the execution traces of a system under verification (SUV), with the purpose of expressing stable conditions in the behaviour of the SUV. The mined formulas represent likely invariants for the SUV, which certainly hold on the considered traces, but there is no guarantee that they are true in general. A large set of representative execution traces must be analysed to increase the probability that mined invariants are generally true. However, this becomes extremely time-consuming for current sequential approaches when long execution traces and large set of SUV variables are considered. To overcome this limitation, the paper presents a parallel approach for invariant mining that exploits GPU architectures for processing an execution trace composed of millions of clock cycles in few seconds.

Breadth-first search (BFS) is one of the most common graph traversal algorithms and the building block for a wide range of graph applications. With the advent of graphics processing units (GPUs), several works have been proposed to accelerate graph algorithms and, in particular, BFS on such many-core architectures. Nevertheless, BFS has proven to be an algorithm for which it is hard to obtain better performance from parallelization. Indeed, the proposed solutions take advantage of the massively parallelism of GPUs but they are often asymptotically less efficient than the fastest CPU implementations. This paper presents BFS-4K, a parallel implementation of BFS for GPUs that exploits the more advanced features of GPU-based platforms (i.e., NVIDIA Kepler) and that achieves an asymptotically optimal work complexity. The paper presents different strategies implemented in BFS-4K to deal with the potential workload imbalance and thread divergence caused by any actual graph non-homogeneity. The paper presents the experimental results conducted on several graphs of different size and characteristics to understand how the proposed techniques are applied and combined to obtain the best performance from the parallel BFS visits. Finally, an analysis of the most representative BFS implementations for GPUs at the state of the art and their comparison with BFS-4K are reported to underline the efficiency of the proposed solution.