  The Sparse GEneral Matrix-Matrix multiplication (SpGEMM) $C = A \times B$ is
a fundamental routine extensively used in domains like machine learning or
graph analytics. Despite its relevance, the efficient execution of SpGEMM on
vector architectures is a relatively unexplored topic. The most recent
algorithm to run SpGEMM on these architectures is based on the SParse
Accumulator (SPA) approach, and it is relatively efficient for sparse matrices
featuring several tens of non-zero coefficients per column as it computes C
columns one by one. However, when dealing with matrices containing just a few
non-zero coefficients per column, the state-of-the-art algorithm is not able to
fully exploit long vector architectures when computing the SpGEMM kernel. To
overcome this issue we propose the SPA paRallel with Sorting (SPARS) algorithm,
which computes in parallel several C columns among other optimizations, and the
HASH algorithm, which uses dynamically sized hash tables to store intermediate
output values. To combine the efficiency of SPA for relatively dense matrix
blocks with the high performance that SPARS and HASH deliver for very sparse
matrix blocks we propose H-SPA(t) and H-HASH(t), which dynamically switch
between different algorithms. H-SPA(t) and H-HASH(t) obtain 1.24$\times$ and
1.57$\times$ average speed-ups with respect to SPA respectively, over a set of
40 sparse matrices obtained from the SuiteSparse Matrix Collection. For the 22
most sparse matrices, H-SPA(t) and H-HASH(t) deliver 1.42$\times$ and
1.99$\times$ average speed-ups respectively.
