Solving Non-binary CSPs Using the Hidden Variable Encoding

Non-binary constraint satisfaction problems (CSPs) can be solved in two different ways. We can either translate the problem into an equivalent binary one and solve it using well-established binary CSP techniques or use extended versions of binary techniques directly on the non-binary problem. Recently, it has been shown that the hidden variable encoding is a promising method of translating non-binary CSPs into binary ones. In this paper we make a theoretical and empirical investigation of arc consistency and search algorithms for the hidden variable encoding. We analyze the potential benefits of applying arc consistency on the hidden encoding compared to generalized arc consistency on the non-binary representation. We also show that search algorithms for nonbinary constraints can be emulated by corresponding binary algorithms that operate on the hidden variable encoding and only instantiate original variables. Empirical results on various implementations of such algorithms reveal that the hidden variable is competitive and in many cases better than the non-binary representation for certain classes of non-binary constraints.