Subset Sum Problems
Why
We consider the case in which the profit and weight function of teh knapsack problem are identical.
Definition
Suppose $(p, w, c)$ is knapsack problem data
and $w = p$.
Then we are interested in finding $x \in
{0,1}^n$ to
\[
\begin{aligned}
\text{maximize} & \quad \textstyle \sum_{i = 1}^{n} q(i)
\chi _{H}(i) \\
\text{subject to} & \quad \textstyle \sum_{i = 1}^{n} w_i
\chi _{H}(i) \leq c
x_i \in \{0,1\}^n \quad i = 1, \dots , n
\end{aligned}
\]