However, the cost of a union of subtrees from different sentences is simply the sum of the costs of subtrees, while the cost of a union of subtrees from the same sentence is smaller than the sum of the costs.
the problem can be represented as follows: For example, if we add a subtree t containing words {w a , w b , w c } to a summary that already covers words {w a , w b , w d } from the same sentence, the additional cost of t is only c({w c }) because w a and w b are already covered 1 .