Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulation that also exploits multiple (intra-node and inter-node) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research

Quantum Algorithms for Finding Constant-sized Sub-hypergraphs

We develop a general framework to construct quantum algorithms that detect if a $3$-uniform hypergraph given as input contains a sub-hypergraph isomorphic to a prespecified constant-sized hypergraph. This framework is based on the concept of nested quantum walks recently proposed by Jeffery, Kothari and Magniez [SODA'13], and extends the methodology designed by Lee, Magniez and Santha [SODA'13] for similar problems over graphs. As applications, we obtain a quantum algorithm for finding a $4$-clique in a $3$-uniform hypergraph on $n$ vertices with query complexity $O(n^{1.883})$, and a quantum algorithm for determining if a ternary operator over a set of size $n$ is associative with query complexity $O(n^{2.113})$.Comment: 18 pages; v2: changed title, added more backgrounds to the introduction, added another applicatio