Abstract
We introduce the Coherent Multi-representation Problem (CMP), whose solutions allow us to observe simultaneously different geometrical representations for the vertices of a given simple graph. The idea of graph multi-representation extends the common concept of graph embedding, where every vertex can be embedded in a domain that is unique for each of them. In the CMP, the same vertex can instead be represented in multiple ways, and the main aim is to find a general multi-representation where all the involved variables are “coherent” with one another. We prove that the CMP extends a geometrical problem known in the literature as the distance geometry problem, and we show a preliminary computational experiment on a protein-like instance, which is performed with a new Java implementation specifically conceived for graph multi-representations.
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Notes
- 1.
https://github.com/mucherino/DistanceGeometry, commit be4e33b, folder javaCMP.
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Acknowledgments
We wish to thank the three reviewers for their fruitful comments. This work is partially supported by ANR French funding agency (multiBioStruct project ANR-19-CE45-0019).
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Mucherino, A. (2023). The Coherent Multi-representation Problem with Applications in Structural Biology. In: Rojas, I., Valenzuela, O., Rojas Ruiz, F., Herrera, L.J., Ortuño, F. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2023. Lecture Notes in Computer Science(), vol 13919. Springer, Cham. https://doi.org/10.1007/978-3-031-34953-9_27
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