Percolationby links appliedto the minimum spanning tree problem

This work shows the procedure to optimize the problem of minimum spanning tree applied to percolation by links problem. The aim is improving the structural quality in a complex network by means of a non-directed graph in a square lattice. Moreover, it defines the size of initial population, the number of edges and the running time for each instance of the proposed problem. Experimental results show that proposed algorithm find good quality solutions efficiently for instances of 10, 100, 200,300,400 and 500 vertices. Tackling an instance of 500 vertices for percolation links problem is an important contribution of this research. This work shows the procedure to optimize the problem of minimum spanning tree applied to percolation by links problem. The aim is improving the structural quality in a complex network by means of a non-directed graph in a square lattice. Moreover, it defines the size of initial population, the number of edges and the running time for each instance of the proposed problem. Experimental results show that proposed algorithm find good quality solutions efficiently for instances of 10, 100, 200,300,400 and 500 vertices. Tackling an instance of 500 vertices for percolation links problem is an important contribution of this research.

[1]  Yan Zhou,et al.  Minimum Spanning Tree Based Clustering Algorithms , 2006, 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06).

[2]  Nikolay V. Dokholyan,et al.  Predicting oil recovery using percolation theory , 2001, Petroleum Geoscience.

[3]  Estefane G. M. de Lacerda,et al.  A genetic algorithm for the capacitated minimum spanning tree problem , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[4]  J. Berg,et al.  A percolation process on the binary tree where large finite clusters are frozen , 2011, 1105.1977.

[5]  Experimental investigations of deterministic chaos appearance in bubbling flow , 2011 .

[6]  Y. Karlovich,et al.  Critical behavior of nanoemitter radiation in a percolation material , 2009 .

[7]  Fangguo He,et al.  A Model and Algorithm for Minimum Spanning Tree Problems in Uncertain Networks , 2008, 2008 3rd International Conference on Innovative Computing Information and Control.

[8]  Yanchun Liang,et al.  A hybrid algorithm of minimum spanning tree and nearest neighbor for classifying human cancers , 2010, 2010 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE).

[9]  Ingo Wegener,et al.  Randomized local search, evolutionary algorithms, and the minimum spanning tree problem , 2004, Theor. Comput. Sci..

[10]  P. Heitjans,et al.  Anomalous Transport and Diffusion in Percolation Systems , 2007 .

[11]  Daniel Horfan Álvarez,et al.  Sistemas de Información Geográfica (SIG) y Teoría de Percolación Aplicados al Estudio de Fenómenos de Propagación en Epidemiología , 2007, Rev. Avances en Sistemas Informática.

[12]  T. Gregory Dewey Fractals in Molecular Biophysics , 1998 .

[13]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[14]  T. S. Jackson,et al.  Theory of minimum spanning trees. II. Exact graphical methods and perturbation expansion at the percolation threshold. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Flow between two sites on a percolation cluster , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Paolo Toth,et al.  The VIII Metaheuristics International Conference id-1 Variable Neighborhood Search for the Cost Constrained Minimum Label Spanning Tree and Label Constrained Minimum Spanning Tree Problems , 2009 .

[17]  M. Vlasova,et al.  Optical percolation in ceramics assisted by porous clusters , 2009 .

[18]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .