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IWOCA
2010
Springer

Computing Role Assignments of Proper Interval Graphs in Polynomial Time

9 years 1 months ago
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.
Pinar Heggernes, Pim van 't Hof, Daniël Paulu
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where IWOCA
Authors Pinar Heggernes, Pim van 't Hof, Daniël Paulusma
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