  We factor Beamer's push-pull, also known as direction-optimized
breadth-first-search (DOBFS) into 3 separable optimizations, and analyze them
for generalizability, asymptotic speedup, and contribution to overall speedup.
We demonstrate that masking is critical for high performance and can be
generalized to all graph algorithms where the sparsity pattern of the output is
known a priori. We show that these graph algorithm optimizations, which
together constitute DOBFS, can be neatly and separably described using linear
algebra and can be expressed in the GraphBLAS linear-algebra-based framework.
We provide experimental evidence that with these optimizations, a DOBFS
expressed in a linear-algebra-based graph framework attains competitive
performance with state-of-the-art graph frameworks on the GPU and on a
multi-threaded CPU, achieving 101 GTEPS on a Scale 22 RMAT graph.
