The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk that starts at a given start node, visits all nodes of the graph, and has the smallest arrival time. In the first and second part of the paper, we consider only undirected temporal graphs that are connected at each time step. For such temporal graphs with n nodes, we show that it is NP-hard to approximate TEXP with ratio $O(n^{1-\epsilon })$ for every $\epsilon >0$ and present several solutions for special graph classes. In the third part of the paper, we consider settings where the graphs in future time steps are not known. We show that m-edge temporal graphs with regularly present edges and with probabilistically present edges can be explored online in $O(m)$ time steps and $O(m\log n)$ time steps with high probability, respectively.

时间图探索问题TEXP是为时间图计算最先探索计划的问题，即从给定的起始节点开始，访问图的所有节点并具有最小到达时间的时间漫游。在本文的第一部分和第二部分中，我们仅考虑在每个时间步长上连接的无向时间图。对于具有这种时间图表Ñ节点，我们表明，它是NP -hard到近似TEXP与比$Ø（{ñ}^{\mathrm{1个}-\epsilon }）$ 每一个 $\epsilon >0$并提供几种特殊图类的解决方案。在本文的第三部分中，我们考虑了不知道未来时间步长图的设置。我们显示可以定期在线浏览具有规则存在的边缘和概率存在的边缘的m边缘时间图$Ø（米）$ 时间步长和 $Ø（米\mathrm{日志}ñ）$ 时间步长的概率很高。