Bounds of the sum of edge lengths in linear arrangements of trees
A fundamental problem in network science is the normalization of the topological or physical distance between vertices, which requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the variation of the physical distance in linear arrangements o...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/345381 |
| Acceso en línea: | https://hdl.handle.net/2117/345381 https://dx.doi.org/10.1088/1742-5468/abd4d7 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Trees (Graph theory) Topology Grafs, Teoria de Arbres (Teoria de grafs) Topologia Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat |
| Sumario: | A fundamental problem in network science is the normalization of the topological or physical distance between vertices, which requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the variation of the physical distance in linear arrangements of the vertices of trees. In particular, we investigate various problems of the sum of edge lengths in trees of a fixed size: the minimum and the maximum value of the sum for specific trees, the minimum and the maximum in classes of trees (bistar trees and caterpillar trees) and finally the minimum and the maximum for any tree. We establish some foundations for research on optimality scores for spatial networks in one dimension. |
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