Interchangeable variables and values

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Interchangeable variables and values • Often variables and values partition interchangeable sets • Timetabling • Class[i]=j iff class i occurs at time j • Classes taken by same students interchangeable (partition into sets) • All times interchangeable
Signature of an assignment • Can break all symmetry due to interchangeable variables and values • By ordering “signatures” of an assignment • Signature is an abstract view of an assignment • Each equivalence class of symmetric assignments has unique signature
Page 1 and 2: Interchangeable variables and value
Page 3 and 4: Types of symmetry • Which part of
Page 5 and 6: Adding constraints • Same method
Page 7: Interchangeable variables and value
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

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