Local Label Propagation

The simplest and most obvious parallel component labeling algorithm proceeds as follows, assuming one lattice site per (abstract) processor.

1. Assign a unique label to each site (e.g., the processor number).
2. Every site looks at its neighbor in the positive x direction.
   If there is a bond between them, and the neighbor's cluster label is smaller than the label at the site in question, then it sets its label to be the same as its neighbor's.
   If the neighbor's label is bigger, then it gets the smaller label.
   This is repeated in the y direction (and other directions in higher dimensions).
3. Repeat the previous step until none of the labels has changed, in which case the clusters have been correctly labeled.