We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be scheduled independently one of another, we consider the setting where the edges are grouped into certain walks (called trips) in the digraph and where assigning the appearing time to the first edge of a trip forces the appearing times of the subsequent edges. In this setting, we show that, quite surprisingly, it is NP-complete to decide whether there exists an assignment of times connecting a given pair of nodes. This result allows us to prove that the problem of maximising the temporal reachability cannot be approximated within a factor better than some polynomial term in the size of the graph. We thus focus on the case where, for each pair of nodes, there exists an assignment of times such that one node is reachable from the other. We call this property strong temporalisability. It is a very natural assumption for the application to public transit networks. On the negative side, the problem of maximising the temporal reachability remains hard to approximate within a factor $\sqrt$ n/12 in that setting. Moreover, we show the existence of collections of trips that are strongly temporalisable but for which any assignment of starting times to the trips connects at most an O(1/ $\sqrt$ n) fraction of all pairs of nodes. On the positive side, we show that there must exist an assignment of times that connects a constant fraction of all pairs in the strongly temporalisable and symmetric case, that is, when the set of trips to be scheduled is such that, for each trip, there is a symmetric trip visiting the same nodes in reverse order. Keywords:edge labeling edge scheduled network network optimisation temporal graph temporal path temporal reachability time assignment

翻译：我们考虑将显示时间的时间分配到测深线边缘的问题, 以便最大限度地实现双节点之间的( 平均) 时间可达性。 由于对公共中转网络的应用程序, 边缘无法单独排列, 我们考虑将边缘分组到测深线的某些行走( 所谓的旅行) 的设置, 将显示时间分到旅行力的第一边缘, 也就是随后边缘的出现时间。 在此设置中, 我们非常惊讶地显示, 将一个时间值与一对结点之间的时间可达性连接起来是完全的。 这样的结果让我们可以证明, 在一个因素中, 将时间可达度最大化的问题无法比图形的某个多位值时间范围更接近。 因此, 我们关注的情况是, 每对一对节点, 将显示一节点与另一节点的可达度。 我们称此属性的短暂可达度, 这是对公共中转网点应用的非常自然的假设。 在负边端, 访问中最接近时间值的轨迹的差不会比 。 最接近时间值的行程将显示一个固定时间值 定期时间值时间值, 我们的行程将显示一个固定时间值 定期的行程将显示一个固定时间值 。