Hierarchical Layout Methods in a Hybrid Framework of Topological Ordering and Graph Grammar

Flowchart layout is of significant value in fields such as software engineering and workflow modeling. However, traditional automatic layout algorithms, including hierarchical layout and force-directed methods, exhibit notable limitations. To address these shortcomings, this paper presents a hybrid optimization framework that integrates graph grammar with topological ordering, aiming to achieve a balance between semantic integrity and computational efficiency. While traditional hierarchical layout algorithms, represented by the Sugiyama framework, eliminate loops by enforcing hierarchical structures, they often compromise the semantic relationships inherent in the original processes. Conversely, force-directed algorithms maintain topological features but face limitations in practical applications due to their computational complexity and stringent constraints on rules. The methodology proposed in this paper is enhanced by the following innovations: Semantics-Driven De-looping and Layering Mechanism: This approach introduces generative rules from graph grammar to remove loops in the original graph structure. Unlike traditional de-looping and layering strategies, which achieve structural optimization through rigid layering, our method relies on rule matching to effectively preserve the semantic integrity of the original processes. Parallelized Implementation of Hierarchical Sorting: This innovation encompasses the hierarchical partitioning of graph structures through topological sorting and graph grammar in both directions, thoroughly considering the topological framework and semantic information embedded within the graphs.