The computational complexity of the partition, 0-1 subset sum, unbounded
subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple
variants were studied in numerous papers in the past where all the weights and
profits were assumed to be integers. We re-examine here the computational
complexity of all these problems in the setting where the weights and profits
are allowed to be any rational numbers. We show that all of these problems in
this setting become strongly NP-complete and, as a result, no pseudo-polynomial
algorithm can exist for solving them unless P=NP. Despite this result we show
that they all still admit a fully polynomial-time approximation scheme.Comment: to appear in Proc. of CSR 201
