Knapsack problem: equal profits

Question

I am looking for references to efficient algorithms that solve knapsack problem where all profits are equal.

More formal definition of the problem from a Wikipedia article on KPs:

If all the profits are 1, we will try to maximize the number of items which would not exceed the knapsack capacity:

maximize $\sum_{j=0}^n x_j$

subject to $\sum_{j=0}^n w_jx_j \leq W$,

$x_j \in \{0, 1\}, \forall_j \in \{1, ..., n\}$

I skimmed through Knapsack Problems book (Kellerer et al', 2004) that is referenced by that Wikipedia article but couldn't find that particular problem.

I also saw some posts about this exact problem with no good answers:

• Knapsack with same value
• Knapsack problem with all profits equal to 1

The answer to the first post mentions Capital Budgeting problem, but the provided link doesn't discuss the case where all profits (values) are equal, which I believe can be better optimized due to its special case.

The answer to the second post mentions a naive solution in which a greedy algorithm picks minimum weight items at each step until no more items fit in the knapsack. This requires knowing the order of items by weight, which results in $O(n\log{n})$ solution.

Is there an algorithm with a better upper bound (e.g. linear time)?