  Self-stabilizing algorithms are an important because of their robustness and
guaranteed convergence. Starting from any arbitrary state, a self-stabilizing
algorithm is guaranteed to converge to a legitimate state.Those algorithms are
not directly amenable to solving distributed graph processing problems when
performance and scalability are important. In this paper, we show the "Abstract
Graph Machine" (AGM) model that can be used to convert self-stabilizing
algorithms into forms suitable for distributed graph processing. An AGM is a
mathematical model of parallel computation on graphs that adds work dependency
and ordering to self-stabilizing algorithms. Using the AGM model we show that
some of the existing distributed Single Source Shortest Path (SSSP) algorithms
are actually specializations of self-stabilizing SSSP. We extend the AGM model
to apply more fine-grained orderings at different spatial levels to derive
additional scalable variants of SSSP algorithms, essentially enabling the
algorithm to be generated for a specific target architecture. Experimental
results show that this approach can generate new algorithmic variants that
out-perform standard distributed algorithms for SSSP.
