Profile minimization on triangulated triangles

Given graph G=(V,E) on n vertices, the profile minimization problem is to find a one-to-one function f: V → {1,2,.....,n} such that Σv ∈ V(G){f(v)-minx ∈ N[v] f(x)} is as small as possible, where N[v] = {v} ∪ {x:x is adjacent to v} is the closed neighborhood of v in G. The trangulated triangle Tl is the graph whose vertices are the triples of non-negative integers summing to l, with an edge connecting two triples if they agree in one coordinate and differ by 1 in the other two coordinates. This paper provides a polynomial time algorithm to solve the profile minimization problem for trangulated triangles Tl with side-length l.