As defined at Wikipedia, UKP is defined as follows:
Let $v_i$ be the given values of the objects, $w_i$ their given weights, $W$ the given maximum weight capacity of the knapsack, and $x_i$ the decision variables that are non-negative integers.
$\max{\sum v_i x_i}$,
subject to $\sum w_i x_i \leq W$ and $x_i \geq 0$.
I want to know if this problem can be solved efficiently when the values are equal to the weights and they are real values. So we would get:
$\max{\sum w_i x_i}$,
subject to $\sum w_i x_i \leq W$ and $x_i \geq 0$.
The decision version of UKP is NP-complete for the general case, but since this is a specific case, I was wondering if it can be solved efficiently. Note that the weights can be real values, so dynamic programming, like shown on Wikipedia would not really work.