Algorithm 1

\(O(\Gamma _l|{\mathcal {P}}||E|)\) time algorithm to compute last2reach(v, i) for all \(v\in V\) and \(i \in [1,|{\mathcal {P}}|]\)
\(O(\Gamma _l|{\mathcal {P}}||E|)\) time algorithm to compute last2reach(v, i) for all \(v\in V\) and \(i \in [1,|{\mathcal {P}}|]\)