One-dimensional search algorithm

set $\xi =0$ , and Φ as a sufficiently large integer

for $\phi =0$ : 1: Φ do

(T,E) = Shortest Path (S₀, D, t, $\xi$ )

//solve the shortest path in terms of delay with a fixed $\xi$

if E ≤ E_max

return T

else

update the offload rate $\xi$ as $\xi +1/\text{Φ}$

end

find the optimal solution ${\xi }^{*}$ for minimal delay $T({\xi }^{*})$