Computing Role Assignments of Proper Interval Graphs in Polynomial Time
A homomorphism from a graph G to a graph R is locally surjective if its restriction to the neighborhood of each vertex of G is surjective. Such a homomorphism is also called an R-role assignment of G. Role assignments have applications in distributed computing, social network theory, and topological graph theory. The Role Assignment problem has as input a pair of graphs (G,R) and asks whether G has an R-role assignment. This problem is NP-complete already on input pairs (G,R) where R is a path on three vertices. So far, the only known non-trivial tractable case consists of input pairs (G,R) where G is a tree. We present a polynomial time algorithm that solves Role Assignment on all input pairs (G,R) where G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that the problem is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.
KeywordsPolynomial Time Connected Graph Maximal Clique Interval Graph Chordal Graph
Unable to display preview. Download preview PDF.
- 1.Angluin, D.: Local and global properties in networks of processors. In: Proceedings of STOC 1980, pp. 82–93. ACM, New York (1980)Google Scholar
- 14.Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. In: Annals of Discrete Mathematics, vol. 57. Elsevier B.V., Amsterdam (2004)Google Scholar
- 20.Reidemeister, K.: Einführung in die kombinatorische Topologie. Braunschweig: Friedr. Vieweg. Sohn A.-G. XII, 209 S (1932)Google Scholar
- 22.Roberts, F.S.: Indifference Graphs. In: Proof Techniques in Graph Theory, pp. 139–146. Academic Press, New York (1969)Google Scholar