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 Bulín et al. [Log. Methods Comput. Sci., 11 (2015)] 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.


  1. discrete optimization
  2. valued constraint satisfaction problems
  3. polymorphisms
  4. fractional polymorphisms

MSC codes

  1. 08A70
  2. 68Q25
  3. 68Q17

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Information & Authors


Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 2279 - 2300
ISSN (online): 1095-7146


Submitted: 5 August 2016
Accepted: 24 July 2017
Published online: 3 October 2017


  1. discrete optimization
  2. valued constraint satisfaction problems
  3. polymorphisms
  4. fractional polymorphisms

MSC codes

  1. 08A70
  2. 68Q25
  3. 68Q17



Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : 714532
Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/L021226/1
Royal Society https://doi.org/10.13039/501100000288

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