Solving finite-domain linear constraints in presence of the $\texttt{alldifferent}$

TL;DR

This paper introduces an improved filtering algorithm for linear constraints in constraint satisfaction problems that leverages alldifferent constraints to achieve stronger bounds and better propagation.

Contribution

The paper presents a novel filtering algorithm that enhances linear constraint solving by exploiting alldifferent constraints, with proven correctness and demonstrated effectiveness.

Findings

The new algorithm produces stronger variable bounds.

Experimental results show improved constraint propagation.

The approach outperforms existing methods in tested problems.

Abstract

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.