Peek Arc Consistency

TL;DR

This paper introduces peek arc consistency, an efficient reasoning technique for constraint satisfaction problems that extends arc consistency with linear space and quadratic time complexity, and can be parallelized for faster solutions.

Contribution

It provides a new, efficient reasoning method called peek arc consistency, with an algebraic characterization and analysis of its applicability to various constraint languages.

Findings

Peek arc consistency runs in quadratic time and linear space.

It offers a polynomial-time decision procedure for certain constraint languages.

The algorithm can be parallelized to achieve linear time with multiple processors.

Abstract

This paper studies peek arc consistency, a reasoning technique that extends the well-known arc consistency technique for constraint satisfaction. In contrast to other more costly extensions of arc consistency that have been studied in the literature, peek arc consistency requires only linear space and quadratic time and can be parallelized in a straightforward way such that it runs in linear time with a linear number of processors. We demonstrate that for various constraint languages, peek arc consistency gives a polynomial-time decision procedure for the constraint satisfaction problem. We also present an algebraic characterization of those constraint languages that can be solved by peek arc consistency, and study the robustness of the algorithm.