GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.Comment: 50 pages, 14 figures, 14 table

Parallel Page Rank Algorithms: A Survey

The PageRank method is an important and basic component in effective web search to compute the rank score of each page. The exponential growth of the Internet makes a crucial challenges for search engines to provide up-to-date and relevant user?s query search results within time period. The PageRank method computed on huge number of web pages and this is computation intensive task. In this paper, we provide the basic concept of PageRank method and discuss some Parallel PageRank methods. We also compare some Parallel algorithmic concepts like load balance, distributed vs. shared memory and data layout on these algorithms

Adaptive image retrieval using a graph model for semantic feature integration

The variety of features available to represent multimedia data constitutes a rich pool of information. However, the plethora of data poses a challenge in terms of feature selection and integration for effective retrieval. Moreover, to further improve effectiveness, the retrieval model should ideally incorporate context-dependent feature representations to allow for retrieval on a higher semantic level. In this paper we present a retrieval model and learning framework for the purpose of interactive information retrieval. We describe how semantic relations between multimedia objects based on user interaction can be learnt and then integrated with visual and textual features into a unified framework. The framework models both feature similarities and semantic relations in a single graph. Querying in this model is implemented using the theory of random walks. In addition, we present ideas to implement short-term learning from relevance feedback. Systematic experimental results validate the effectiveness of the proposed approach for image retrieval. However, the model is not restricted to the image domain and could easily be employed for retrieving multimedia data (and even a combination of different domains, eg images, audio and text documents)

A Web Aggregation Approach for Distributed Randomized PageRank Algorithms

The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are treated as agents computing their own PageRank by communicating with linked pages. This paper builds upon this approach to reduce the computation and communication loads for the algorithms. In particular, we develop a method to systematically aggregate the web pages into groups by exploiting the sparsity inherent in the web. For each group, an aggregated PageRank value is computed, which can then be distributed among the group members. We provide a distributed update scheme for the aggregated PageRank along with an analysis on its convergence properties. The method is especially motivated by results on singular perturbation techniques for large-scale Markov chains and multi-agent consensus.Comment: To appear in the IEEE Transactions on Automatic Control, 201

Acceleration of Histogram-Based Contrast Enhancement via Selective Downsampling

In this paper, we propose a general framework to accelerate the universal histogram-based image contrast enhancement (CE) algorithms. Both spatial and gray-level selective down- sampling of digital images are adopted to decrease computational cost, while the visual quality of enhanced images is still preserved and without apparent degradation. Mapping function calibration is novelly proposed to reconstruct the pixel mapping on the gray levels missed by downsampling. As two case studies, accelerations of histogram equalization (HE) and the state-of-the-art global CE algorithm, i.e., spatial mutual information and PageRank (SMIRANK), are presented detailedly. Both quantitative and qualitative assessment results have verified the effectiveness of our proposed CE acceleration framework. In typical tests, computational efficiencies of HE and SMIRANK have been speeded up by about 3.9 and 13.5 times, respectively.Comment: accepted by IET Image Processin

Acceleration of PageRank with customized precision based on mantissa segmentation

[EN] We describe the application of a communication-reduction technique for the PageRank algorithm that dynamically adapts the precision of the data access to the numerical requirements of the algorithm as the iteration converges. Our variable-precision strategy, using a customized precision format based on mantissa segmentation (CPMS), abandons the IEEE 754 single- and double-precision number representation formats employed in the standard implementation of PageRank, and instead handles the data in memory using a customized floating-point format. The customized format enables fast data access in different accuracy, prevents overflow/underflow by preserving the IEEE 754 double-precision exponent, and efficiently avoids data duplication, since all bits of the original IEEE 754 double-precision mantissa are preserved in memory, but re-organized for efficient reduced precision access. With this approach, the truncated values (omitting significand bits), as well as the original IEEE double-precision values, can be retrieved without duplicating the data in different formats. Our numerical experiments on an NVIDIA V100 GPU (Volta architecture) and a server equipped with two Intel Xeon Platinum 8168 CPUs (48 cores in total) expose that, compared with a standard ieee double-precision implementation, the CPMS-based PageRank completes about 10% faster if high-accuracy output is needed, and about 30% faster if reduced output accuracy is acceptable.H. Anzt was supported by the "Impuls und Vernetzungsfond" of the Helmholtz Association under grant VH-NG-1241. G. Flegar and E. S. Quintana-Orti were supported by project TIN2017-82972-R of the MINECO and FEDER. This work was also supported by the EU H2020 project 732631 "OPRECOMP. Open Transprecision Computing,' and the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Numbers DE-SC0016513 and DE-SC-0010042Gruetzmacher, T.; Cojean, T.; Flegar, G.; Anzt, H.; Quintana-Orti, ES. (2020). Acceleration of PageRank with customized precision based on mantissa segmentation. ACM Transactions on Parallel Computing. 7(1):1-19. https://doi.org/10.1145/3380934S1197

Agents, Bookmarks and Clicks: A topical model of Web traffic

Analysis of aggregate and individual Web traffic has shown that PageRank is a poor model of how people navigate the Web. Using the empirical traffic patterns generated by a thousand users, we characterize several properties of Web traffic that cannot be reproduced by Markovian models. We examine both aggregate statistics capturing collective behavior, such as page and link traffic, and individual statistics, such as entropy and session size. No model currently explains all of these empirical observations simultaneously. We show that all of these traffic patterns can be explained by an agent-based model that takes into account several realistic browsing behaviors. First, agents maintain individual lists of bookmarks (a non-Markovian memory mechanism) that are used as teleportation targets. Second, agents can retreat along visited links, a branching mechanism that also allows us to reproduce behaviors such as the use of a back button and tabbed browsing. Finally, agents are sustained by visiting novel pages of topical interest, with adjacent pages being more topically related to each other than distant ones. This modulates the probability that an agent continues to browse or starts a new session, allowing us to recreate heterogeneous session lengths. The resulting model is capable of reproducing the collective and individual behaviors we observe in the empirical data, reconciling the narrowly focused browsing patterns of individual users with the extreme heterogeneity of aggregate traffic measurements. This result allows us to identify a few salient features that are necessary and sufficient to interpret the browsing patterns observed in our data. In addition to the descriptive and explanatory power of such a model, our results may lead the way to more sophisticated, realistic, and effective ranking and crawling algorithms.Comment: 10 pages, 16 figures, 1 table - Long version of paper to appear in Proceedings of the 21th ACM conference on Hypertext and Hypermedi