Dear all,

I have the shortest path problem coded in JuMP as follows:

```
using JuMP
import HiGHS
import LinearAlgebra
G = [
0 100 30 0 0
0 0 20 0 0
0 0 0 10 60
0 15 0 0 50
0 0 0 0 0
]
n = size(G)[1]
shortest_path = Model(HiGHS.Optimizer)
@variable(shortest_path, x[1:n, 1:n], Bin)
@constraint(shortest_path, [i = 1:n, j = 1:n; G[i, j] == 0], x[i, j] == 0)
@constraint(
shortest_path,
[i = 1:n; i != 1 && i != 2],
sum(x[i, :]) == sum(x[:, i])
)
@constraint(shortest_path, sum(x[1, :]) - sum(x[:, 1]) == 1)
@constraint(shortest_path, sum(x[2, :]) - sum(x[:, 2]) == -1)
@objective(shortest_path, Min, LinearAlgebra.dot(G, x))
optimize!(shortest_path)
```

that works perfectly. However, I would like to re-write this code creating only the variables where a arc existis, e.g., not create n x n binay variables and set to zero all where `G[i,j] =0`

.

My idea is determine the indexes `i`

and `j`

whose G[i,j] >0, as follows:

```
ind = findall(G .> 0)
7-element Array{CartesianIndex{2},1}:
CartesianIndex(1, 2)
CartesianIndex(4, 2)
CartesianIndex(1, 3)
CartesianIndex(2, 3)
CartesianIndex(3, 4)
CartesianIndex(3, 5)
CartesianIndex(4, 5)
```

Thatâ€™s ok. But, now, how can I create the variable `x[i,j]`

where `i`

and `j`

belongs to aray `ind`

So I create only the necessary variables and constraintsâ€¦

Thank ypou so much for the help.