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In this paper we propose a vectorized sorted set intersection approach for the task of counting the exact number of triangles of a graph on CPU cores. The computation is factorized into reordering and counting kernels where the reordering kernel builds upon the Reverse Cuthill-McKee heuristic.
For problems of image or video segmentation, where clusters have a complex structure, a leading method is spectral clustering. It works by encoding the similarity between pairs of points into an affinity matrix and applying k-means in its low-order eigenspace, where the clustering structure is enhanced. When the number of points is large, an approximation is necessary to limit the runtime even if...
Many modern highly scalable scientific simulations packages rely on small matrix multiplications as their main computational engine. Math libraries or compilers are unlikely to provide the best possible kernel performance. To address this issue, we present a library which provides high performance small matrix multiplications targeting all recent x86 vector instruction set extensions up to Intel AVX-512...
Sparse matrix-vector multiplication (SpMV) is an important computational kernel in many applications. For performance improvement, software libraries designated for SpMV computation have been introduced, e.g., MKL library for CPUs and cuSPARSE library for GPUs. However, the computational throughput of these libraries is far below the peak floating-point performance offered by hardware platforms, because...
Numerous applications focus on the analysis of entities and the connections between them, and such data are naturally represented as graphs. In particular, the detection of a small subset of vertices with anomalous coordinated connectivity is of broad interest, for problems such as detecting strange traffic in a computer network or unknown communities in a social network. Eigenspace analysis of large-scale...
We implement a promising algorithm for sparse-matrix sparse-vector multiplication (SpMSpV) on the GPU. An efficient k-way merge lies at the heart of finding a fast parallel SpMSpV algorithm. We examine the scalability of three approaches -- no sorting, merge sorting, and radix sorting -- in solving this problem. For breadth-first search (BFS), we achieve a 1.26x speedup over state-of-the-art sparse-matrix...
We present a new Gaussian process (GP) inference algorithm, called online sparse matrix Gaussian processes (OSMGP), and demonstrate its merits by applying it to the problems of head pose estimation and visual tracking. The OSMGP is based upon the observation that for kernels with local support, the Gram matrix is typically sparse. Maintaining and updating the sparse Cholesky factor of the Gram matrix...
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