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What is the risk of adding symmetry breaking constraints?

  • A.They always make the problem harder to propagate
  • B.They increase the number of variables in the problem
  • C.They can only be added once a solution has already been found
  • D.They may exclude every solution if incorrectly formulated

Answer: D

A constraint intended to keep one representative must be shown to leave at least one member of each equivalence class, or the problem becomes unsatisfiable although solutions exist. That is easy to get wrong when several symmetries interact. Propagation usually improves, the variable count is unchanged, and the constraints are added before searching. A modification justified by an argument must have that argument checked, since the failure is silent and looks like an insoluble problem.

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