Variable and value elimination in binary constraint satisfaction via forbidden patterns

TL;DR

This paper characterizes the fundamental variable and value elimination rules in binary CSPs using forbidden patterns, introducing three new rules that generalize neighborhood substitution and enhance preprocessing techniques.

Contribution

It identifies only four variable and three value elimination rules based on forbidden patterns, including three novel rules that extend existing methods.

Findings

Four key variable elimination rules identified, including the known Broken Triangle Property.

Three new value elimination rules introduced, generalizing neighborhood substitution.

Elimination rules enable polynomial-time preprocessing without affecting satisfiability.

Abstract

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.