Symmetry Breaking Using Value Precedence

TL;DR

This paper explores the use of value precedence constraints for breaking value symmetry in constraint satisfaction problems, offering efficient encodings and extensions to handle complex symmetries, and analyzing their interactions with other symmetry-breaking methods.

Contribution

It introduces an efficient encoding of value precedence constraints, extends them to complex symmetries, and analyzes their relationship with lexicographical ordering and variable symmetry breaking.

Findings

Efficient encoding of value precedence constraints.

Extensions to wreath value and partial interchangeability.

Analysis of interactions with variable symmetry breaking.

Abstract

We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreath value and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries.