Uma Abordagem Estatística para o Projeto de Topologias Físicas de Redes Ópticas - Depizzol, Daniela Bertolini (2018)
Optical networks play a vital role in the current information society, and this puts thedesign of such networks as a central issue. Poor design of an optical network can leadto wasted resources and poor network performance. Many parameters can indicate thecharacteristics of a network, and among them there is the minimum number of wavelengths(λ) required to meet a given traffic demand, which is a dominant cost factor in networkdesigning, where its optimization maximizes the spectrum available on the network. Anatural modeling for optical networks is by means of graphs, which have a number ofnodes (n) and edges (m). The number of possible networks grows exponentially withn,which makes difficult to find networks that minimizeλ, what is aggravated by the factthat the calculation ofλis a NP-Hard problem. With the hypothesis that the value ofλto be influenced by the network topology, it is sought to find topological invariantsof graphs with polynomial computational time, that are well correlated withλ, and sothatλcan be estimated more quickly, as a function of these invariants. In the presentwork, it is proceeded with an exploratory search of graphs topological invariants, in thebest of efforts. Such raised base of invariants is ranked, in an unprecedented selectionof attributes in optical networks, via mutual information estimators. For this, a samplewith2.2×106random networks that mimic real networks is used, where the invariantsranking occurs with all networks together and also separated byn. As a result, stand outthe invariants derived fromedge betweenness, which are among the best positioned in theobtained rankings, demonstrating their good representativeness to explainλ. Then, fromthe most significant invariants to explainλ, it is proceeded with appropriate regressionsto estimateλ. This estimation facilitates theλtest in a large number of graphs and isconsidered in heuristics to search, in a few minutes, for topologies that minimize therequirement for wavelengths. The total savings between the real input networks and theiroutput networks varies from 23% to 59% and, in addition, output networks demonstrategreater reliability compared to real input networks.