Interchangeable variables and values

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Dynamic methods • “Efficient” dynamic methods exist for interchangeable variables and values • Dominance detection between two assignments in O(nd+d 5/2 ) time • Eliminate all symmetry at each node in O(nd 7/2 +n 2 d 2 ) time • Not seen this implemented!
Conclusions • Symmetry occurs in many problems • We must deal with it or face a combinatorial explosion! • We have a generic method (for small numbers of symmetries) • In special cases, we can break all symmetries • One such case is when vars and vals partition into interchangeable sets
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 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: Some special cases • All variable

Interchangeable variables and values

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