Algorithm 1 Dedicated Path Protection Algorithm

In: graph G, source vertex s, target vertex t

Out: a cheapest pair of paths, and their CUs

Here, we concentrate on permanent solutions $n_x$.

$x_s=(s,s)$ $x_t=(t,t)$ $l_{x_s}=((0,\Omega ),(0,\Omega ))$ $n_{x_s}=(x_s,l_{x_s},e_{\varnothing },\mathrm{null})$ $T_{x_s}=\left\{n_{x_s}\right\}$ $push(Q,(0,n_{x_s}))$ whileQ is not empty do $n_x=pop\left(Q\right)$      if $n_x==\mathrm{null}$ then           continue the main loop $x=(v_{x,1},v_{x,2})=vertex\left(n_x\right)$      // Remove $n_x$ from the set of tentative solutions for x. $T_x=T_x-\left\{n_x\right\}$      // Add $n_x$ to the set of permanent solutions for x. $P_x=P_x\cup \left\{n_x\right\}$      if $x==x_t$ then           break the main loop $l_x=(p_{x,1},p_{x,2})=label\left(n_x\right)$      for each out edge $e^{\prime }$ of vertex $v_{x,1}$ in G do $relax(e^{\prime },v_{x,2},p_{x,2},p_{x,1},n_x)$      for each out edge $e^{\prime }$ of vertex $v_{x,2}$ in G do $relax(e^{\prime },v_{x,1},p_{x,1},p_{x,2},n_x)$ return$trace(P,x_t,x_s)$