  We study methods for transforming valued constraint satisfaction problems
(VCSPs) to binary VCSPs. First, we show that the standard dual encoding
preserves many aspects of the algebraic properties that capture the
computational complexity of VCSPs. Second, we extend the reduction of CSPs to
binary CSPs described by Bulin et al. [LMCS'15] to VCSPs. This reduction
establishes that VCSPs over a fixed valued constraint language are
polynomial-time equivalent to Minimum-Cost Homomorphism Problems over a fixed
digraph.
