Bellman-Ford algorithm

d[s] <- 0
for each v ∈ V-{s}
	do d[v] <- ∞

for i <- 1 to |V|-1
	do for each edge (u,v)∈E
		do if d[v] > d[u] + w(u,v)
			then d[v] <- d[u] = w(u,v) //relaxation step
for each edge(u,v)∈E
	do if d[v]>d[u]+w(w,v)
		then report that a negative-weight cycle exists

At the end, d[v] = δ(s,v), if no negative-weight cycles.
Time = O(VE)