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What is symmetry breaking in a constraint problem?

  • A.Assigning all of the symmetric variables the same value throughout
  • B.Ordering the variables so that symmetry is preserved
  • C.Adding constraints to exclude equivalent copies of a solution
  • D.Removing constraints that make the problem symmetric

Answer: C

If relabelling colours or reflecting a board produces another solution, the search wastes effort exploring every copy, and adding an ordering constraint keeps only one representative of each class. Care is needed not to exclude all solutions. Constraint removal, forced equality and ordering for preservation are different operations. Recognising that a search is exploring the same thing many times over, and forbidding the duplicates, can reduce the work by an enormous factor.

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