Dijkstra's Algorithm [1959] (nonnegative weights only)

Q = V
S = {}
repeat
select a vertex u from Q
Use to update other values
S = S $\cup$ {u}
until Q = {}

• Use priority queue for Q with d(v) as the key
  • Extract-Min to select from Q
  • Decrease-Key to change d(v)

• Greedy choice for next vertex to add to S (contains vertices whose shortest path is known)
  • Because of optimal substructure