Abstract Graph Machine

TL;DR

The paper introduces the Abstract Graph Machine (AGM), a formal model for analyzing distributed memory parallel graph algorithms that ensures correct execution order through work dependency and strict weak ordering.

Contribution

It presents the AGM model, its semantics, and applies it to several existing distributed memory parallel graph algorithms, providing a formal framework.

Findings

AGM formalizes work dependencies in parallel graph algorithms.

AGM models ensure correct processing order with strict weak ordering.

Application of AGM to existing algorithms demonstrates its utility.

Abstract

An Abstract Graph Machine(AGM) is an abstract model for distributed memory parallel stabilizing graph algorithms. A stabilizing algorithm starts from a particular initial state and goes through series of different state changes until it converges. The AGM adds work dependency to the stabilizing algorithm. The work is processed within the processing function. All processes in the system execute the same processing function. Before feeding work into the processing function, work is ordered using a strict weak ordering relation. The strict weak ordering relation divides work into equivalence classes, hence work within a single equivalence class can be processed in parallel, but work in different equivalence classes must be executed in the order they appear in equivalence classes. The paper presents the AGM model, semantics and AGM models for several existing distributed memory parallel graph algorithms.