Recursive Solution

• d_ij^(k) = weight of eventually shortest path from i to j with all intermediate vertices in {1, 2, .., k}
• 
  
  $$d_{ij}^{(k)} \;=\; \left\{ \begin{array}{lll} w_{ij} & {\rm i... ...+\; d_{kj}^{(k-1)}) & {\rm if} & k \geq 1 \end{array} \right.$$
  
  

• , n = $\mid$V$\mid$