Preference CSPs

Given a partial solution to a CSP, how could we use this to get an optimistic bound?

c o w **

b o o

Across:

• 1: cow (9), pig (7)
• 3: boo (2), egg (7)

Down:

• 1: cub (3), pie (3)
• 2: woo (3), gag (3)

Many possibilities:

• Assume maximum score for all slots [11+18].
• For each slot, assume maximum score for that slot [11+6].
• For each slot, assume maximum score for that slot, factoring in existing constraints [unsat].