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

### Morihiro Hayashida, Hitoshi Koyano, Tatsuya Akutsu

#### Abstract

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 series-parallel 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.

#### References

#### Paper Citation

#### in Harvard Style

Hayashida M., Koyano H. and Akutsu T. (2018). **Grammar-based Compression for Directed and Undirected Generalized Series-parallel Graphs using Integer Linear Programming**.In *Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOINFORMATICS,* ISBN 978-989-758-280-6, pages 105-111. DOI: 10.5220/0006583001050111

#### in Bibtex Style

@conference{bioinformatics18,

author={Morihiro Hayashida and Hitoshi Koyano and Tatsuya Akutsu},

title={Grammar-based Compression for Directed and Undirected Generalized Series-parallel Graphs using Integer Linear Programming},

booktitle={Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOINFORMATICS,},

year={2018},

pages={105-111},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006583001050111},

isbn={978-989-758-280-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 4: BIOINFORMATICS,

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

SN - 978-989-758-280-6

AU - Hayashida M.

AU - Koyano H.

AU - Akutsu T.

PY - 2018

SP - 105

EP - 111

DO - 10.5220/0006583001050111