Strengthening neighbourhood substitution

TL;DR

This paper introduces strengthened forms of neighbourhood substitution for binary CSPs, which can be applied efficiently but are NP-hard to optimize globally, enhancing constraint reduction techniques.

Contribution

It proposes two strengthened variants of neighbourhood substitution that do not increase computational complexity and proves the NP-hardness of finding optimal sequences of these operations.

Findings

Strengthened substitution methods improve domain reduction.

Optimal sequence determination is NP-hard.

No increase in time complexity for applying the new methods.

Abstract

Domain reduction is an essential tool for solving the constraint satisfaction problem (CSP). In the binary CSP, neighbourhood substitution consists in eliminating a value if there exists another value which can be substituted for it in each constraint. We show that the notion of neighbourhood substitution can be strengthened in two distinct ways without increasing time complexity. We also show the theoretical result that, unlike neighbourhood substitution, finding an optimal sequence of these new operations is NP-hard.