Partitioning Algorithms for a Span Classsearchtermclassspan of Knapsack
Partitioning Algorithms for a Span Classsearchtermclassspan of Knapsack
John F John Franklin Pierce
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- s s Proof of the theorem follows from the fact that since the sets D and D are complementary an optimal solution for every length L must be contained in at least one of the sets. For each un- evaluated length L, B(L) constitutes the maximum value attainable among solutions in D ; hence, for any unevaluated length L*. If O "" i V(L*) is the maximum value attainable among solutions in D ^ ™" X then F(L*) = max [B{L*), V(L*)j. Therefore since solution A is — A optimal among solutions D _ for len...gth L it is by Theorem 2, optimal among solutions D for all lengths L(A )
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