Let $S = \{\{x_{11},x_{12},x_{13}\},\{x_{21},x_{22},x_{23}\}, \ldots, \{x_{n1},x_{n2},x_{n3}\}\}$ and a target $t$. Let $S_i$ be the subset list $\{x_{i1},x_{i2},x_{i3}\}$. Find a subset sum that sums to $t$ such that one and only one element is chosen from each subset list $S_i$.

I can also imagine this is the same as finding the longest path from $s$ to some sink such that the path costs less than $t$, where the sum of the edges is the same as choosing from each subset list $S_i$.

Is there a name for this problem? Thanks.

Let $S = \{\{x_{1},y_{1},z_{1}\},\{x_{2},y_{2},z_{2}\}, \ldots, \{x_{n},y_{n},z_{n}\}\}$ and a target $t$. Let $S_i$ be the subset list $\{x_{i},y_{i},z_{i}\}$. Find a subset sum that sums to $t$ such that one and only one element is chosen from each subset list $S_i$.

I can also imagine this is the same as finding the longest path from $s$ to some sink such that the path costs less than $t$, where the sum of the edges is the same as choosing from each subset list $S_i$.

Is there a name for this problem? Thanks.

Let S = {{x_11,x_12,x_13},{x_21,x_22,x_23}, ...., {x_n1,x_n2,x_n3}} and target t. Let S_i be the subset list {x_i1,x_i2,x_i3}. Find a subset sum that sums to t such that one and only one element is chosen from each subset list S_i.

I can also imagine this is the same as finding the longest path from s to some sink such that the path cost less than t. Where the sum of the edges is the same as the choosing from each subset list S_i.

Is there a name for this problem? Thanks.

Let $S = \{\{x_{11},x_{12},x_{13}\},\{x_{21},x_{22},x_{23}\}, \ldots, \{x_{n1},x_{n2},x_{n3}\}\}$ and a target $t$. Let $S_i$ be the subset list $\{x_{i1},x_{i2},x_{i3}\}$. Find a subset sum that sums to $t$ such that one and only one element is chosen from each subset list $S_i$.

I can also imagine this is the same as finding the longest path from $s$ to some sink such that the path costs less than $t$, where the sum of the edges is the same as choosing from each subset list $S_i$.

Is there a name for this problem? Thanks.