# Families of Distributed Memory Parallel Graph Algorithms from Self-Stabilizing Kernels-An SSSP Case Study

## TL;DR

This paper introduces the AGM model to transform self-stabilizing algorithms into scalable distributed graph algorithms, specifically for SSSP, demonstrating improved performance over standard methods.

## Contribution

The paper presents the AGM model that converts self-stabilizing algorithms into distributed graph algorithms and extends it for architecture-specific optimization.

## Key findings

- AGM model effectively converts self-stabilizing algorithms for distributed graph processing.
- Derived SSSP variants outperform standard distributed algorithms in experiments.
- Fine-grained orderings enable architecture-specific scalable algorithm generation.

## Abstract

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.