Solving the Sensitivity Problem with TIE

Solving the problem with our mechanism requires us to find values of $\alpha(i,p,e)$ and $\beta(i,p,e)$, for each $i,e \in N$ and $p\in P$, that lead to the desired egress-point selections over all graph transformations $\Delta G$. Our solution has two main steps. First, a simulation phase determines the desired egress selection both at design time (under graph $G$) and after each topology change (under graph $\delta(G)$). The output of this phase is a set of constraints on the $\alpha$ and $\beta$ values for each $(i,p)$ pair. Then, an optimization phase determines the values of $\alpha$ and $\beta$ that satisfy these constraints. For this problem, the egress-point selection for each $(i,p)$ pair can be made independently.