Interchangeable variables and values

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Symmetry breaking • General method for variable symmetries [Crawford, Ginsberg, Luks and Roy KR96] • Look for lexicographically least assignment • (Z[1],Z[2],...) ≤lex (Z[σ(1)],Z[σ(2)],...) • reversal symmetry: (X[1],X[2],...,X[n-1],X[n]) ≤lex (X[n],X[n-1],...,X[2],X[1])
Adding constraints • Same method works with symmetries in general [Walsh CP06] • Including those that act both on variables and values simultaneously • Look for assignment that is lex smaller than all its symmetries • So, we’re done? Symmetry solved problem?
Page 1 and 2: Interchangeable variables and value
Page 3: Types of symmetry • Which part of
Page 7 and 8: Interchangeable variables and value
Page 9 and 10: Signature of an assignment • Can
Page 11 and 12: Signature of an assignment • Supp
Page 13 and 14: Signature of an assignment • Sign
Page 15 and 16: Ordering signatures • To break al
Page 17 and 18: • • Variables partition into tw
Page 19 and 20: Ordering signatures • Equivalent
Page 21 and 22: Some special cases • All variable
Page 23 and 24: Conclusions • Symmetry occurs in

Interchangeable variables and values

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