Bilateração e Geometria de Distâncias

• Ano de defesa: 2022
• Autor(a) principal: Bezerra, Antonielle Gomes
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; Brasil; Programa de Pós-graduação em Matemática (Mestrado Profissional)
• Palavras-chave em Português: Bilateração; Bilateration; Geometria de Distâncias; Distance Geometry; Distâncias Euclidianas; Euclidean Distances; Completamento de Matrizes; Matrix Completion; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA; Matemática; Geometria; Algoritmos
• Link de acesso: https://repositorio.ufu.br/handle/123456789/34036; http://doi.org/10.14393/ufu.di.2022.6

Recently, the euclidean distance geometry problems of DMDGP2 type have been solved by calculation techniques based on discrete variables for matrices completion, applying the Cayley-Menger determinants to solve this kind of problem. In this work we delineate algorithms using successive bilaterations to complete the partial matrix associated to the DMDGP2 instance. The algorithm is similar to the BP: Branch-And-Prune algorithm, explorig the tree of possibilities generated by bilaterations and making use of recursivity techniques of back-tracking type to find the solutions. On respect to the proposed algorithm validation, all the expected solution-matrices were found, in compliance to the respective obtained Cayley-Menger determinants calculation.