Algorithm 2 relax

In: edge $e^{\prime }$, const vertex $v_1$, const trait $p_1$, other trait $p_2$,

previous search-tree node $n_x$

Here, we concentrate on tentative solutions $n_{x^{\prime }}$.

$v^{\prime }=target\left(e^{\prime }\right)$ $c^{\prime }=cost\left(\mathrm{path}\mathrm{of}{p}_2\mathrm{with}{e}^{\prime }\mathrm{appended}\right)$ for each CU $C^{\prime }$ in $CU\left(p_2\right)\cap AU\left(e^{\prime }\right)$ do $x^{\prime }=(v_1,v^{\prime })$ $p^{\prime }=(c^{\prime },C^{\prime })$      if $decide\left(p^{\prime }\right)$ then $l_{x^{\prime }}=(p_1,p^{\prime })$          if $v^{\prime }<v_1$ then $swap\left(x^{\prime }\right)$ $swap\left(l_{x^{\prime }}\right)$          else if $v_1==v^{\prime }$ and not $p_1\le p^{\prime }$ then $swap\left(l_{x^{\prime }}\right)$           // Make sure we should be interested in $l_{x^{\prime }}$.           if $\nexists n\in P_{x^{\prime }}:label\left(n\right)\le l_{x^{\prime }}$ then                if $\nexists n\in T_{x^{\prime }}:label\left(n\right)\le l_{x^{\prime }}$ then                     // Make sure we are not reusing $e^{\prime }$.                     if $e^{\prime }$ not used by ancestors then                         // Discard worse tentative solutions. $T_{x^{\prime }}=T_{x^{\prime }}-\{n\in T_{x^{\prime }}:l_{x^{\prime }}\le label\left(n\right)\}$ $n_{x^{\prime }}=(x^{\prime },l_{x^{\prime }},e^{\prime },n_x)$                         // Add $n_{x^{\prime }}$ to the tentative solutions for $x^{\prime }$. $T_{x^{\prime }}=T_{x^{\prime }}\cup \left\{n_{x^{\prime }}\right\}$ $push(Q,(COST\left(l_{x^{\prime }}\right),n_{x^{\prime }}))$