Adaptive sparse matrix-matrix multiplication on the GPU. Martin Winter, Daniel Mlakar, Rhaleb Zayer, Hans-Peter Seidel, and Markus Steinberger. 2019.
In the ongoing efforts targeting the vectorization of linear algebra primitives, sparse matrix-matrix multiplication (SpGEMM) has received considerably less attention than sparse Matrix-Vector multiplication (SpMV). While both are equally important, this disparity can be attributed mainly to the additional formidable challenges raised by SpGEMM. In this paper, we present a dynamic approach for addressing SpGEMM on the GPU. Our approach works directly on the standard compressed sparse rows (CSR) data format. In comparison to previous SpGEMM implementations, our approach guarantees a homogeneous, load-balanced access pattern to the first input matrix and improves memory access to the second input matrix. It adaptively re-purposes GPU threads during execution and maximizes the time efficient on-chip scratchpad memory can be used. Adhering to a completely deterministic scheduling pattern guarantees bit-stable results during repetitive execution, a property missing from other approaches. Evaluation on an extensive sparse matrix benchmark suggests our approach being the fastest SpGEMM implementation for highly sparse matrices (80% of the set). When bit-stable results are sought, our approach is the fastest across the entire test set.
Layered fields for natural tessellations on surfaces. Rhaleb Zayer, Daniel Mlakar, Markus Steinberger, and Hans-Peter Seidel. 2018.
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced with challenging issues such as metric estimation, geometric, topological complications, and most critically, parallelization. In this paper, we introduce an alternate model which may be of value for resolving these issues. We drop the assumption that regions need to be separated by lines. Instead, we regard region boundaries as narrow bands and we model the partition as a set of smooth functions layered over the surface. Given an initial set of seeds or regions, the partition emerges as the solution of a time dependent set of partial differential equations describing concurrently evolving fronts on the surface. Our solution does not require geodesic estimation, elaborate numerical solvers, or complicated bookkeeping data structures. The cost per time-iteration is dominated by the multiplication and addition of two sparse matrices. Extension of our approach in a Lloyd’s algorithm fashion can be easily achieved and the extraction of the dual mesh can be conveniently preformed in parallel through matrix algebra. As our approach relies mainly on basic linear algebra kernels, it lends itself to efficient implementation on modern graphics hardware.
faimGraph: high performance management of fully-dynamic graphs under tight memory constraints on the GPU. Martin Winter, Daniel Mlakar, Rhaleb Zayer, Hans-Peter Seidel, and Markus Steinberger.
In this paper, we present a fully-dynamic graph data structure for the Graphics Processing Unit (GPU). It delivers high update rates while keeping a low memory footprint using autonomous memory management directly on the GPU. The data structure is fully-dynamic, allowing not only for edge but also vertex updates. Performing the memory management on the GPU allows for fast initialization times and efficient update procedures without additional intervention or reallocation procedures from the host. Our optimized approach performs initialization completely in parallel; up to 300x faster compared to previous work. It achieves up to 200 million edge updates per second for sorted and unsorted update batches; up to 30x faster than previous work. Furthermore, it can perform more than 300 million adjacency queries and millions of vertex updates per second. On account of efficient memory management techniques like a queuing approach, currently unused memory is reused later on by the framework, permitting the storage of tens of millions of vertices and hundreds of millions of edges in GPU memory. We evaluate algorithmic performance using a PageRank and a Static Triangle Counting (STC) implementation, demonstrating the suitability of the framework even for memory access intensive algorithms.