LAHypergraph: Parallel Hypergraph Analytics in the Language of Linear Algebra

Hypergraphs are recently emerging as a robust set-theoretical mathematical tool that can faithfully model higher-order relationships among the entities in a dataset. To design efficient and portable algorithms for hypergraphs, we consider the adjacency matrix and the incidence matrix representations of a hypergraph. An adjacency matrix (clique-expansion)-based hypergraph algorithm formulation has a one-to-one correspondence with processing a unipartite graph. However, in addition to large memory footprint, the adjacency matrix representation loses structural information about the original hypergraph. In contrast, an incidence matrix-based hypergraph algorithm formulation operates on a bipartite graph view of the modeled dataset. The incidence matrix representation retains both the hyperedge set and the vertex set information of a hypergraph and has lower memory footprint. Considering these facts, in this paper, we propose a suite of parallel, portable hypergraph algorithms, composed with a set of sparse linear algebra-based operations, especially for incidence matrix-based hypergraph processing. We identify the semiring operations for generalized sparse matrix-vector multiplication (SpMV) and the pattern of their applications, which are the main foundations of these algorithms. Implementations of our linear algebra based hypergraph algorithms for both the CPUs and the GPUs are included in a library, namely LAHypergraph. From a performance viewpoint, we demonstrate that our incidence matrix based algorithms in LAHypergraph on the GPUs outperform the state-of-the-art (SOTA) Hygra framework. From the portability viewpoint, thanks to the composition of our algorithms with only a handful of sparse linear algebra operations, our approach is amenable to easy porting to new parallel hardwares.