The maximum saving partition problem

The input to the MAXIMUM SAVING PARTITION PROBLEM consists of a set V={1,...,n}, weights w"i, a function f, and a family S of feasible subsets of V. The output is a partition (S"1,...,S"l) such that S"[email protected]?S, and @?"j"@?"Vw"[email protected]?"i"="1^lf(S"i) is maximized. We present a general 12-approximation algorithm, and improved algorithms for special cases of the function f.

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