Extension of Hoshen–Kopelman algorithm to non-lattice environments

Abstract We extend the Hoshen–Kopelman (HK) algorithm for cluster labeling to non-lattice environments, where sites are placed at random at non-lattice points. This extension is useful for continuum systems and disordered networks. Our extension of the HK algorithm relies on several data structures that describe network connectivity regardless of its dimensionality. Just as for the classic HK algorithm on lattices, our extension is completed in a single pass through the sites of the network and cluster relabeling operates on a vector whose size is much smaller than the size of the network. Our extension of the HK algorithm works for any environment (lattice or non-lattice) of any dimensionality, type (sites, bonds or both), and with arbitrary connectivity between the sites. The proposed extension is illustrated through a simple network consisting of 16 sites and 24 bonds, and applied to a complex network extracted from a 3D micro-focused X-ray CT image of Bentheimer sandstone consisting of 3677 sites and 8952 bonds.

[1]  Tadeusz W Patzek,et al.  Verification of a Complete Pore Network Simulator of Drainage and Imbibition , 2001 .

[2]  D. C. Rapaport,et al.  Cluster size distribution at criticality , 1992 .

[3]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[4]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[5]  David Wilkinson,et al.  Invasion percolation: a new form of percolation theory , 1983 .

[6]  J. Hoshen,et al.  Percolation and cluster structure parameters: The enhanced Hoshen-Kopelman algorithm , 1997 .

[7]  J. M. Teuler,et al.  A direct parallel implementation of the Hoshen-Kopelman algorithm for distributed memory architectures , 2000 .

[8]  H. Stanley,et al.  Download details: , 1983 .

[9]  Tadeusz W Patzek,et al.  Impact of wettability alteration on two‐phase flow characteristics of sandstones: A quasi‐static description , 2003 .

[10]  J. Hoshen.  Percolation analog for a two-component liquid-vapor system , 1980 .

[11]  D. Rapaport.  Cluster number scaling in two-dimensional percolation , 1986 .

[12]  D. Wilkinson,et al.  Percolation with trapping , 1986 .

[13]  Harvey Gould,et al.  An Introduction to Computer Simulation Methods: Applications to Physical Systems , 2006 .

[14]  P. Tamayo,et al.  Parallel cluster labeling for large-scale Monte Carlo simulations , 1995 .

[15]  Joseph Hoshen,et al.  Percolation and cluster distribution. III. Algorithms for the site-bond problem , 1979 .

[16]  J. Mariani,et al.  Transient synaptic redundancy in the developing cerebellum and isostatic random stacking of hard spheres , 1996, Biological Cybernetics.

[17]  Sally J. Marshall,et al.  The X-ray tomographic microscope: Three-dimensional perspectives of evolving microstructures , 1994 .

[18]  Lee,et al.  Monte Carlo study of correlated continuum percolation: Universality and percolation thresholds. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[19]  O. I. Yordanov,et al.  Classification of radar signatures by autoregressive model fitting and cluster analysis , 1989 .

[20]  Harvey Gould,et al.  An Introduction to Computer Simulation Methods: Applications to Physical Systems (3rd Edition) , 2005 .

[21]  Simulation of catalyst fouling at the particle and reactor levels , 1996 .

[22]  Raoul Kopelman,et al.  Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm , 1976 .

[23]  Rosana G. Moreira,et al.  Spatial distribution of oil after deep-fat frying of tortilla chips from a stochastic model , 1996 .

[24]  Michael W. Berry,et al.  Parallelization of the Hoshen-Kopelman Algorithm Using a Finite State Machine , 1997, Int. J. High Perform. Comput. Appl..

[25]  Joseph Hoshen,et al.  On the application of the enhanced Hoshen-Kopelman algorithm for image analysis , 1998, Pattern Recognit. Lett..

[26]  Paul R. Wellin,et al.  Computer simulations with Mathematica - explorations in complex physical and biological systems , 1995 .

[27]  E. T. Gawlinski,et al.  Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs , 1981 .

[28]  Wil G. M. Geraets,et al.  Analysis of the radiographic trabecular pattern , 1991, Pattern Recognit. Lett..

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

[30]  I. Orgzall,et al.  Universality and cluster structures in continuum models of percolation with two different radius distributions , 1993 .

[31]  Anthony N. Burkitt,et al.  Parallelization of a cluster algorithm , 1989 .