Hoshen–Kopelman algorithm: Difference between revisions

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The Hoshen-Kopelman Algorithm is simple and efficient algorithm for labeling [[Cluster_analysis | clusters]] on a grid, where grid is a regular network of cells, where each cell may be <strong>occupied</strong> or <strong>unoccupied</strong>. This algorithm is based on well-known union-finding algorithm. The algorithm was originally described in [http://journals.aps.org/prb/abstract/10.1103/PhysRevB.14.3438 Percolation and Cluster Distribution. I. Cluster Multiple Labeling Technique and Critical Concentration Algorithm] by J. Hoshen and R. Kopelman.<ref>http://journals.aps.org/prb/abstract/10.1103/PhysRevB.14.3438</ref>

== Percolation Theory ==

[[Percolation_theory|Percolation Theory]] is the study of the behavior and statistics of clusters on [[Lattice_graph | lattices]]. Suppose we have a large square lattice where each cell can be occupied with the [[Probability | probability]] <code>p</code> and empty with probability <code>1 – p</code>. Each group of neighboring occupied cells forms a cluster. Neighbors are defined as cells having a common side but not those sharing only a corner i.e. we consider 4x4 neighborhood. (top, bottom, left, right). Each occupied cell is occupied independently of the status of its neighborhood. The number of clusters, size of each cluster and their distribution are important topics in Percolation Theory.

[[File:Occupied Grids P=0.24.png|thumb|Occupied Grids P = 0.24]]

== Hoshen - Kopelman Algorithm for cluster finding ==

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== Example ==

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== Applications ==