Compaction, retraction, and constraint satisfaction
In this paper, we show a very close relationship among the compaction, retraction, and constraint satisfaction problems in the context of reflexive and bipartite graphs. The compaction and retraction problems are special graph coloring problems, and the constraint satisfaction problem is well known to have an important role in artificial intelligence. The relationships we present provide evidence that, similar to the retraction problem, it is likely to be difficult to determine whether for every fixed reflexive or bipartite graph, the compaction problem is polynomial time solvable or NP-complete. In particular, the relationships that we present relate to a long-standing open problem concerning the equivalence of the compaction and retraction problems.
compaction retraction constraint satisfaction graph coloring computational complexity homomorphism