1. What are the contributions in this paper?
The authors study methods for transforming valued constraint satisfaction problems ( VCSPs ) to binary VCSPs.. First, the authors show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity of VCSPs.. Second, the authors extend the reduction of CSPs to binary CSPs described by Buĺın et al. [ LMCS ’ 15 ] to VCSPs.
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2. What are the future works in this paper?
In order to study families of valued constraint languages with finitely many cost functions defined by fractional polymorphisms satisfying linear balanced identities, the authors now know that they need only study MinCostHom problems.. This is important since, for example, to prove the algebraic dichotomy conjecture for core crisp languages the authors only need to study polymorphisms satisfying linear balanced identities [ 6 ].. Their contribution is to show that the CSP reduction from [ 14 ] can be extended to the more general setting of the VCSP, and that the extended reduction preserves all linear balanced identities.. The authors believe that their extension of this reduction can also be adapted to derive similar conclusions, but they leave this as an open problem.
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