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Normalization by second order graphs: A visual alternative to simplify systems

Normalización mediante grafos de Segundo orden: una alternativa visual para simplificar sistemas

Edward Muñoz Garro

This issue stems from the need for tools to analyze and make decisions around complex systems, where they apply the rules for linearly dependent sets, with the purpose of providing a visual tool, which serves to support complexity reduction processes. Two great precedents are Armstrong´s Axioms, which has been applied from its publication to the present for database normalization, the other is set theory, a fundamental pillar of the Structured Query Language; based on them, together with the second-order logic, which adds qualifiers for subsets or properties, this work has been prepared, with an explanatory metrology with a qualitative approach, in an axiomatic system. As a result, a support tool has been provided to analyze complex systems naturally, by breaking cycles and detecting patterns, without interfering with existing models; however, for large systems it can be difficult to address it in its entirety, so it is recommended to divide by subsystems. With this work a technique has been accomplished, repeatable by anyone, but with a strong theoretical foundation. This work has great utility for the normalization of relational databases and an enormous potential for application in the design of systems beyond computational systems, it is also useful for understanding dependencies by their axiomatic nature.@en

Este tema nace de la necesidad de herramientas para analizar y tomar decisiones en torno a sistemas complejos, donde apliquen las reglas para conjuntos linealmente dependientes, con el fin de proporcionar una herramienta visual, que sirva de apoyo a procesos de reducción de la complejidad. Dos grandes precedentes son los Axiomas de W. Armstrong, el cual se ha aplicado desde su publicación hasta la actualidad para la normalización de bases de datos, el otro es la teoría de conjuntos, pilar fundamental del Lenguaje de Consultas Estructurado; en base a ellos, junto con la lógica de segundo orden, la cual añade cualificadores para subconjuntos o propiedades se ha elaborado este trabajo, con una metrología explicativa con enfoque cualitativo, en un sistema axiomático. Como resultado se ha proporciona una herramienta de soporte para analizar sistemas complejos de forma natural, rompiendo ciclos y detectando patrones, sin interferir con los modelos existentes; sin embargo, para sistemas de gran tamaño puede ser difícil abordarlo en su totalidad, por lo que se recomienda dividir por subsistemas. Con este trabajo se ha consumado una técnica, repetible por cualquiera, pero con fuerte fundamento teórico. Este trabajo tiene gran utilidad para la normalización de bases de datos relacionales y un enorme potencial de aplicación en el diseño de sistemas más allá de los sistemas computacionales, también resulta útil para la comprensión de dependencias por su naturaleza axiomática.@es

References

  • Armstrong, W., Nakamura, Y., & Rudnicki, P. (2002). Armstrong’s axioms. Journal of formalized Mathematics, 14(1). DOI:10.1.1.77.8348
  • Attallah, B. (2017). Simplifying Database Normalization within a Visual Interactive Simulation Model. International Journal Of Database Management Systems, 9(3), 57-69. doi: 10.5121/ijdms.2017.9304
  • Bondy, J. A., & Murty (1976) Graph theory with applications. Retrieved from https://pdfs.semanticscholar.org/56a1/3467a3cfb7a9ec00b7f3ed5e953324225233.pdf
  • Frisendal, T. (2020). Visual Normalization – Use the Power of the Dependencies. Retrieved from https://www.dataversity.net/visual-normalization-use-power-dependencies/#
  • Kumar, D., Raj, A., & Dharanipragada, J. (2017). GraphSteal: Dynamic Re-Partitioning for Efficient Graph Processing in Heterogeneous Clusters. In 2017 IEEE 10Th International Conference On Cloud Computing (CLOUD). doi: 10.1109/cloud.2017.63
  • Ren, J., Schneider, J., Ovsjanikov, M., & Wonka, P. (2017). Joint Graph Layouts for Visualizing Collections of Segmented Meshes. In IEEE transactions on visualization and computer graphics, 24(9), 2546-2558. DOI: 10.1109/TVCG.2017.2751473.
  • Shi, Q., Liu, G., Zheng, K., Liu, A., Li, Z., Zhao, L., & Zhou, X. (2017). Multi-Constrained Top-K Graph Pattern Matching in Contextual Social Graphs. In 2017 IEEE International Conference On Web Services (ICWS). DOI: 10.1109/icws.2017.69
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