Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

TL;DR

This paper evaluates binary encodings of non-binary CSPs, demonstrating that specialized algorithms can outperform traditional non-binary methods in certain cases, supported by theoretical and empirical evidence.

Contribution

It introduces specialized arc consistency and search algorithms for binary encodings of non-binary CSPs, showing their effectiveness over standard binary techniques.

Findings

Binary encodings can be competitive for certain non-binary constraints

Standard binary CSP techniques often perform poorly on encoded non-binary problems

Specialized algorithms improve performance of binary encodings

Abstract

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally accepted that the translated problem can be solved by applying well-established techniques for binary CSPs. In this paper we evaluate the applicability of the latter approach. We demonstrate that the use of standard techniques for binary CSPs in the encodings of non-binary problems is problematic and results in models that are very rarely competitive with the non-binary representation. To overcome this, we propose specialized arc consistency and search algorithms for binary encodings, and we evaluate them theoretically and empirically. We consider three binary representations; the hidden variable encoding, the dual encoding, and the double encoding. Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation.