As we know, an unbounded knapsack problem could be described as:$\max \sum_{i=1}^nc_1x_i$s.t. $\sum_{i=1}^na_ix_i\le b$$x_i\ge0,x_i\in\mathbb Z,i=1,\cdots,n$And for an 0-1 knapsack problem, we have an additional restriction:$x_i\in\{0,1\},i=1,\cdots,n$However, I would like to know whether there exists a reduction from the 0-1 knapsack problem to the unbounded knapsack problem?I have thought over this problem, but I could not imagine whether something could be done in the unbounded problem in order to simulate the effect as the constraint $x_i\in\{0,1\}$ in a 0-1 knapsack problem.Thanks!
Is there a reduction from a 0-1 knapsack problem to the unbounded problem?
np hardness;reductions;np;integer programming;np complete