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.

Ning Li. Hierarchical Layout Methods in a Hybrid Framework of Topological Ordering and Graph Grammar. Academic Journal of Computing & Information Science(2025), Vol. 8, Issue 3: 87-94. https://doi.org/10.25236/AJCIS.2025.080312.

[1] TUTTE W T.How to draw a graph[J].Proceedings of the London Mathematical Society, 1963, 3(1): 743-767.

[2] EADES P.A heuristic for graph drawing[J].Congressus Numerantium, 1984, 42: 149-160.

[3] KAMADA T, KAWAI S.An algorithm for drawing general undirected graphs[J].Information Processing Letters, 1989, 31(1): 7-15.

[4] FRUCHTERMAN T M J, REINGOLD E M.Graph drawing by force‐directed placement[J]. Software: Practice and Experience, 1991, 21(11): 1129-1164.

[5] DAVIDSON R, HAREL D.Drawing graphs nicely using simulated annealing[J].ACM Transactions on Graphics, 1996, 15(4): 301-331.

[6] NOACK A.An energy model for visual graph clustering[C]//Proceedings of the 11th International Symposium on Graph Drawing, Perugia, 2003: 425-436.

[7] JACOMY M, VENTURINI T, HEYMANN S, et al.ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the Gephi software[J].PLoS ONE, 2014, 9(6): e98679.

[8] HADANY R, HAREL D.A multi-scale algorithm for drawing graphs nicely[J].Discrete Applied Mathematics, 2001, 113(1): 3-21.

[9] WALSHAW C.A multilevel algorithm for force-directed graph drawing[C]//Proceedings of the 8th International Symposium on Graph Drawing, Heidelberg, 2000: 171-182.

[10] HACHUL S, JÜNGER M. Large-graph layout algorithms at work: an experimental study[J]. Journal of Graph Algorithms and Applications, 2007, 11(21): 345-369.

[11] HOLTEN D, VAN WIJK J J.A user study on visualizing directed edges in graphs[C]//Proceedings of the 2019 SIGCHI Conference on Human Factors in Computing Systems, Boston, 2009: 2299-2308.

[12] HUANG W. Establishing aesthetics based on human graph reading behavior: two eye tracking studies[J].Personal & Ubiquitous Computing, 2013, 17(1): 93-105.

[13] PURCHASE H C. Metrics for graph drawing aesthetics[J].Journal of Visual Languages & Computing, 2002, 13(5): 501-516.