Algorithm 1 . The algorithm below updates all affected nodes, and edges, whenever there is a change in any node.

stack $\leftarrow [startEdge]$

$visited\leftarrow []$

while stack do

for all neighbor_edge $\in$ graph.edges(edge[1]) do

if neighbor_edge $\notin$ visited then

visited.append(neighbor_edge)

if edge $\notin$ parent[neighbor_edge] then

parent[neighbor_edge].append(edge)

cost $\leftarrow$ weight_cost[edge] + graph[neighbor_edge][‘weight’]

weight_cost[neighbor_edge] + = cost

end if

end if

end for

end while