The min-cut and vertex separator problem

Rendl, Franz; Sotirov, Renata

doi:10.1007/s10589-017-9943-4

Cited by 18 publications

(23 citation statements)

References 39 publications

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“…Because the original VSP is considered as NP-Hard [8,63], the adaptation from multiplex networks, is NP-Hard too [64,65]; therefore, we can solve the adaptation of VSP using a heuristic method.…”

Section: B Methodsmentioning

confidence: 99%

Identification of COVID-19 Spreaders Using Multiplex Networks Approach

et al. 2020

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In this work, we present a methodology to identify COVID-19 spreaders using the analysis of the relationship between socio-cultural and economic characteristics with the number of infections and deaths caused by the COVID-19 virus in different countries. For this, we analyze the information of each country using the complex networks approach, specifically by analyzing the spreaders countries based on the separator set in 5-layer multiplex networks. The results show that, we obtain a classification of the countries based on their numerical values in socioeconomics, population, Gross Domestic Product (GDP), health and air connections; where, in the spreader set there are those countries that have high, medium or low values in the different characteristics; however, the aspect that all the countries belonging to the separator set share is a high value in air connections. INDEX TERMS Complex networks, complex systems, COVID-19, multiplex networks, optimization, social networks.

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Section: B Methodsmentioning

confidence: 99%

Identification of COVID-19 Spreaders Using Multiplex Networks Approach

et al. 2020

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“…Because the original VSP is considered NP-hard [46,47], the adaptation from multiplex networks is NP-hard too [48,49]; therefore, we can solve the adaptation of VSP using a heuristic method.…”

Section: Simulated Annealing To Solve M-vspmentioning

confidence: 99%

Inverse Percolation to Quantify Robustness in Multiplex Networks

et al. 2020

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Inverse percolation is known as the problem of finding the minimum set of nodes whose elimination of their links causes the rupture of the network. Inverse percolation has been widely used in various studies of single-layer networks. However, the use and generalization of multiplex networks have been little considered. In this work, we propose a methodology based on inverse percolation to quantify the robustness of multiplex networks. Specifically, we present a modified version of the mathematical model for the multiplex-vertex separator problem (m-VSP). By solving the m-VSP, we can find nodes that cause the rupture of the mutually connected giant component (MCGC) and the large viable cluster (LVC) when their links are removed from the network. The methodology presented in this work was tested in a set of benchmark networks, and as case study, we present an analysis using a set of multiplex social networks modeled with information about the main characteristics of the best universities in the world and the universities in Mexico. The results show that the methodology presented in this work can work in different models and types of 2- and 3-layer multiplex networks without dividing the entire multiplex network into single-layer as some techniques described in the specific literature. Furthermore, thanks to the fact that the technique does not require the calculation of some structural measure or centrality metric, and it is easy to scale for networks of different sizes.

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“…The optimal bi-partitioning of a graph is the one that minimizes such cut value. Even though there exist a large number of such partitions, finding the minimum cut of a graph is a well-studied problem and there exist efficient algorithms for solving it (Rendl & Sotirov, 2018).…”

Section: Normalized Cut (Ncut)mentioning

confidence: 99%

Gradient-based Learning Methods Extended to Smooth Manifolds Applied to Automated Clustering

Koudounas¹,

Fiori

2020

jair

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Grassmann manifold based sparse spectral clustering is a classification technique that consists in learning a latent representation of data, formed by a subspace basis, which is sparse. In order to learn a latent representation, spectral clustering is formulated in terms of a loss minimization problem over a smooth manifold known as Grassmannian. Such minimization problem cannot be tackled by one of traditional gradient-based learning algorithms, which are only suitable to perform optimization in absence of constraints among parameters. It is, therefore, necessary to develop specific optimization/learning algorithms that are able to look for a local minimum of a loss function under smooth constraints in an efficient way. Such need calls for manifold optimization methods. In this paper, we extend classical gradient-based learning algorithms on at parameter spaces (from classical gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means of tools from manifold calculus. We compare clustering performances of these methods and known methods from the scientific literature. The obtained results confirm that the proposed learning algorithms prove lighter in computational complexity than existing ones without detriment in clustering efficacy.

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The min-cut and vertex separator problem

Cited by 18 publications

References 39 publications

Identification of COVID-19 Spreaders Using Multiplex Networks Approach

Identification of COVID-19 Spreaders Using Multiplex Networks Approach

Inverse Percolation to Quantify Robustness in Multiplex Networks

Gradient-based Learning Methods Extended to Smooth Manifolds Applied to Automated Clustering

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