Computing Role Assignments of Proper Interval Graphs in Polynomial Time

  • Pinar Heggernes
  • Pim van ’t Hof
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


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.


Polynomial Time Connected Graph Maximal Clique Interval Graph Chordal Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Pim van ’t Hof
    • 2
  • Daniël Paulusma
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.School of Engineering and Computing Sciences, Science LaboratoriesDurham UniversityDurhamEngland

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