These algorithms proceed in two phases -- local coloring and conflict resolution. The local coloring tentatively colors all vertices at the distance required given what's known of the global coloring. Then, the updated colors are transferred to different processors at distance one. In the distance one case, each vertex with nonlocal neighbors is then checked to see if it conforms, with the vertex being marked for recoloring if its lower weight than its same colored neighbor. In the distance two case, each boundary vertex's immediate star is checked for validity of the coloring. Lower-weight conflict vertices are marked, and then the conflicts are gathered back on owning processors. In both cases this is done until each column has received a valid color.