Variable Elimination in Binary CSP via Forbidden Patterns

A variable elimination rule allows the polynomial-time identification of certain variables whose elimination does not affect the satisfiability of an instance. Variable elimination in the constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. We show that there are essentially just four variable elimination rules defined by forbidding generic sub-instances, known as irreducible patterns, in arc-consistent CSP instances. One of these rules is the Broken Triangle Property, whereas the other three are novel.