min weight of a simple path from to using nodes in {1, 2, ..., }
That is, the new shortest path is either the previous shortest path or the shortest path that includes the node that we have just added to our available list.
![\( D \left[u, v, k\right] = \)](img5.png){kind=small}
min weight of a simple path from 
to 
using nodes in {1, 2, ..., 
}
![\( \tilde{D} \left[u, v, k\right] = \min \left\{ D \left[u, v, k-1\right], D \left[u, k, k-1\right] + \tilde{D} \left[k, v, k-1\right] \right\} \)](img8.png){kind=small}