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Graphs are ubiquitous, and they can model unique characteristics and complex relations of real-life systems. Although using machine learning (ML) on graphs is promising, their raw representation is not suitable for ML algorithms. Graph embedding represents each node of a graph as a d-dimensional vector which is more suitable for ML tasks. However, the embedding process is expensive, and CPU-based tools do not scale to real-world graphs. In this work, we present GOSH, a GPU-based tool for embedding large-scale graphs with minimum hardware constraints. GOSH employs a novel graph coarsening algorithm to enhance the impact of updates and minimize the work for embedding. It also incorporates a decomposition schema that enables any arbitrarily large graph to be embedded with a single GPU. As a result, GOSH sets a new state-of-the-art in link prediction both in accuracy and speed, and delivers high-quality embeddings for node classification at a fraction of the time compared to the state-of-the-art. For instance, it can embed a graph with over 65 million vertices and 1.8 billion edges in less than 30 minutes on a single GPU., Comment: 12 pages, 11 tables, 6 figures, submitted for publication at Special Section on Parallel and Distributed Computing Techniques for AI, ML, and DL

Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric applications, this data is streaming; new items arrive continuously, and the data grows with time. With paradigms such as Internet of Things and Edge Computing, such applications become more natural and more practical. In this work, we assume a streaming model where the data is modeled as a hypergraph, which is generated at the edge. This data then partitioned and sent to remote nodes via an algorithm running on a memory-restricted device such as a single board computer. Such a partitioning is usually performed by taking a connectivity metric into account to minimize the communication cost of later analyses that will be performed in a distributed fashion. Although there are many offline tools that can partition static hypergraphs excellently, algorithms for the streaming settings are rare. We analyze a well-known algorithm from the literature and significantly improve its running time by altering its inner data structure. For instance, on a medium-scale hypergraph, the new algorithm reduces the runtime from 17800 seconds to 10 seconds. We then propose sketch- and hash-based algorithms, as well as ones that can leverage extra memory to store a small portion of the data to enable the refinement of partitioning when possible. We experimentally analyze the performance of these algorithms and report their run times, connectivity metric scores, and memory uses on a high-end server and four different single-board computer architectures., Comment: 8 pages, 6 algorithms, 2 figures, 4 tables, submitted to HPCS'20

In graph embedding, the connectivity information of a graph is used to represent each vertex as a point in a d-dimensional space. Unlike the original, irregular structural information, such a representation can be used for a multitude of machine learning tasks. Although the process is extremely useful in practice, it is indeed expensive and unfortunately, the graphs are becoming larger and harder to embed. Attempts at scaling up the process to larger graphs have been successful but often at a steep price in hardware requirements. We present GOSH, an approach for embedding graphs of arbitrary sizes on a single GPU with minimum constraints. GOSH utilizes a novel graph coarsening approach to compress the graph and minimize the work required for embedding, delivering high-quality embeddings at a fraction of the time compared to the state-of-the-art. In addition to this, it incorporates a decomposition schema that enables any arbitrarily large graph to be embedded using a single GPU with minimum constraints on the memory size. With these techniques, GOSH is able to embed a graph with over 65 million vertices and 1.8 billion edges in less than an hour on a single GPU and obtains a 93% AUCROC for link-prediction which can be increased to 95% by running the tool for 80 minutes., Comment: 11 pages, 4 figures, published in ICPP 2020: The 49th International Conference on Parallel Processing - Edmonton, AB, Canada

Influence maximization (IM) is the problem of finding a seed vertex set which is expected to incur the maximum influence spread on a graph. It has various applications in practice such as devising an effective and efficient approach to disseminate information, news or ad within a social network. The problem is shown to be NP-hard and approximation algorithms with provable quality guarantees exist in the literature. However, these algorithms are computationally expensive even for medium-scaled graphs. Furthermore, graph algorithms usually suffer from spatial and temporal irregularities during memory accesses, and this adds an extra cost on top of the already expensive IM kernels. In this work, we leverage fused sampling, memoization, and vectorization to restructure, parallelize and boost their performance on undirected networks. The proposed approach employs a pseudo-random function and performs multiple Monte-Carlo simulations in parallel to exploit the SIMD lanes effectively and efficiently. Besides, it significantly reduces the number of edge traversals, hence the amount of data brought from the memory, which is critical for almost all memory-bound graph kernels. We apply the proposed approach to the traditional MixGreedy algorithm and propose Infuser which is more than 3000 times faster than the traditional greedy approaches and can run on large graphs that have been considered as too large in the literature., Comment: 12 pages, 6 figures. Submitted to IEEE Transactions on Parallel and Distributed Systems

In parallel computing, a valid graph coloring yields a lock-free processing of the colored tasks, data points, etc., without expensive synchronization mechanisms. However, coloring is not free and the overhead can be significant. In particular, for the bipartite-graph partial coloring (BGPC) and distance-2 graph coloring (D2GC) problems, which have various use-cases within the scientific computing and numerical optimization domains, the coloring overhead can be in the order of minutes with a single thread for many real-life graphs. In this work, we propose parallel algorithms for bipartite-graph partial coloring on shared-memory architectures. Compared to the existing shared-memory BGPC algorithms, the proposed ones employ greedier and more optimistic techniques that yield a better parallel coloring performance. In particular, on 16 cores, the proposed algorithms perform more than 4x faster than their counterparts in the ColPack library which is, to the best of our knowledge, the only publicly-available coloring library for multicore architectures. In addition to BGPC, the proposed techniques are employed to devise parallel distance-2 graph coloring algorithms and similar performance improvements have been observed. Finally, we propose two costless balancing heuristics for BGPC that can reduce the skewness and imbalance on the cardinality of color sets (almost) for free. The heuristics can also be used for the D2GC problem and in general, they will probably yield a better color-based parallelization performance especially on many-core architectures., Comment: 11 pages

We design, implement, and evaluate GPU-based algorithms for the maximum cardinality matching problem in bipartite graphs. Such algorithms have a variety of applications in computer science, scientific computing, bioinformatics, and other areas. To the best of our knowledge, ours is the first study which focuses on GPU implementation of the maximum cardinality matching algorithms. We compare the proposed algorithms with serial and multicore implementations from the literature on a large set of real-life problems where in majority of the cases one of our GPU-accelerated algorithms is demonstrated to be faster than both the sequential and multicore implementations., Comment: 14 pages, 5 figures