Variable and value elimination in binary constraint satisfaction via forbidden patterns
This work provides incremental theoretical insights into preprocessing for constraint satisfaction, primarily benefiting researchers in AI and optimization.
The paper tackled the problem of reducing search space in binary constraint satisfaction problems by identifying variable and value elimination rules that do not affect satisfiability, showing there are essentially four variable and three such rules based on forbidden patterns, with three variable rules being novel.
Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time identification of certain variables (domain elements) whose elimination, without the introduction of extra compensatory constraints, does not affect the satisfiability of an instance. We show that there are essentially just four variable elimination rules and three value elimination rules defined by forbidding generic sub-instances, known as irreducible existential patterns, in arc-consistent CSP instances. One of the variable elimination rules is the already-known Broken Triangle Property, whereas the other three are novel. The three value elimination rules can all be seen as strict generalisations of neighbourhood substitution.