Profile minimization on triangulated triangles

  • Authors:

  • Yuqiang Guan;Kenneth L. Williams

  • Affiliations:

  • Department of Computer Science, University of Texas, Austin, TX;Department of Computer Science, Western Michigan University, Kalamazoo, MI

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

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Abstract

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.