A Generalized Arc-Consistency Algorithm for a Class of Counting Constraints: Revised Edition that Incorporates One Correction

TL;DR

This paper presents a generalized arc-consistency algorithm for the SEQ BIN meta-constraint, enabling efficient encoding of counting constraints like CHANGE, SMOOTH, and INCREASING NVALUE with improved computational complexity.

Contribution

It introduces a new meta-constraint and a polynomial-time algorithm that enforces generalized arc-consistency for counting constraints, optimizing time and space complexity.

Findings

GAC can be enforced with linear time and space complexity for certain constraints

The algorithm improves or matches the best known results in literature

Applicable to encoding various counting constraints efficiently

Abstract

This paper introduces the SEQ BIN meta-constraint with a polytime algorithm achieving general- ized arc-consistency according to some properties. SEQ BIN can be used for encoding counting con- straints such as CHANGE, SMOOTH or INCREAS- ING NVALUE. For some of these constraints and some of their variants GAC can be enforced with a time and space complexity linear in the sum of domain sizes, which improves or equals the best known results of the literature.