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We address a problem of finding generation rules from biological data, especially, represented as directed and undirected generalized series-parallel graphs (GSPGs), which include trees, outerplanar graphs, and seriesparallel graphs. In the previous study, grammars for edge-labeled rooted ordered and unordered trees, called SEOTG and SEUTG, respectively, were defined, and it was examined to extract generation rules from glycans and RNAs that can be represented by rooted tree structures, where integer linear programming-based methods for finding the minimum SEOTG and SEUTG that produce only given trees were developed. In nature and organisms, however, there are various kinds of structures such as gene regulatory networks, metabolic pathways, and chemical structures that cannot be represented as rooted trees. In this study, we relax the limitation of structures to be compressed, and propose grammars representing edge-labeled directed and undirected GSPGs based on context-free grammars by extending SEOTG and SEUTG. In addition, we propose an integer linear programming-based method for finding the minimum GSPG grammar in order to analyze more complicated biological networks and structures.

Grammar-based Compression for Directed and Undirected Generalized Series-parallel Graphs using Integer Linear Programming