We consider the online multiple Steiner Traveling Salesman Problem based on the background of the delivery of packages in an urban traffic network. In this problem, given an edge-weighted undirected graph \(G = (V, E)\), a subset \(D\subset V\) of customer vertices, and m salesmen. For each edge in E, the weight w(e) is associated with the traversal time or the cost of the edge. The aim is to find m closed tours that visit each vertex of D at least once. We formulate the traffic congestion with k non-recoverable blocked edges revealed to the salesmen in real-time, meaning that the salesmen know about a blocked edge whenever it occurs. For the version to minimize the maximum cost of m salesmen (minmax mSTSP), we prove a lower bound and propose the ForestTraversal algorithm. The corresponding competitive ratio is proved to be linear with k. For the version to minimize the total cost of m salesmen (minsum mSTSP), we also propose a lower bound and the Retrace algorithm, where the competitive ratio of the algorithm is proved to be linear with k.

我们基于城市交通网络中包裹递送的背景来考虑在线多个Steiner Traveling Salesman问题。在此问题中，给定边缘加权无向图\（G =（V，E）\），客户顶点的子集\（D \子集V \）和m个销售员。对于E中的每个边缘，权重w（e）与遍历时间或边缘成本相关联。目的是找到m个闭合行程，这些行程至少访问D的每个顶点。我们用k来表示交通拥堵不可恢复的阻塞边缘会实时向销售人员显示，这意味着销售人员会在发生阻塞边缘时就知道它。对于最小化m个销售人员的最大成本（minmax mSTSP）的版本，我们证明了一个下限，并提出了ForestTraversal算法。证明相应的竞争率与k呈线性关系。对于最小化m个销售人员的总成本（minsum mSTSP）的版本，我们还提出了一个下限和Retrace算法，其中该算法的竞争比被证明与k成线性关系。