An efficient algorithm for a class of constraint satisfaction problems

We define the class of the so-called monotone constraint satisfaction problems (MON-CSP). MON-CSP forms a subclass of the class of min-closed (respectively, max-closed) constraint satisfaction problems of Jeavons and Cooper (Artificial Intelligence 79 (1995) 327). We prove that for all problems in the class MON-CSP there exists a very fast and very simple algorithm for testing feasibility. We then show that a number of well-known results from the literature are special cases of MON-CSP: (1) Satisfiability of Horn formulae; (2) graph homomorphisms to directed graphs with an -numbering; (3) monotone integer programming with two variables per inequality; (4) project scheduling under AND/OR precedence constraints. Our results provide a unified algorithmic approach to all these problems.