Computing role assignments of proper interval graphs in polynomial time

  • Authors:

  • Pinar Heggernes;Pim van 't Hof;Daniël Paulusma

  • Affiliations:

  • Department of Informatics, University of Bergen, Bergen, Norway;School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, England;School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, England

  • Venue:
  • IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
  • Year:
  • 2010

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Abstract

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.