与无限容量的车辆共乘
Ride Sharing with a Vehicle of Unlimited Capacity
摘要：
考虑了一个乘车共享问题，其中我们给出了一个图，其边缘配备了旅行成本，加上一组对象，每个对象与一对起点和目的地节点给出的运输请求相关联。一辆车在图中行驶，将每个物体从其起点运送到目的地，而不限制可以同时运输的物体数量。车辆在给定的节点开始和终止其行程，目标是计算满足所有请求的最小成本行程。通过设计一个$O(h \log h+n)$算法，其中$h$是不同请求的数目，$n$是路径中节点的数目，该算法被用作一个子程序来有效地求解定义在循环上的实例，从而覆盖所有具有最大度$2$的图.这跟踪了易处理性的边界，因为$\bf NP$ -硬实例在最大度为$3$的树上展示。
英文摘要：
A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle travels through the graph, carrying each object from its origin to its destination without any bound on the number of objects that can be simultaneously transported. The vehicle starts and terminates its ride at given nodes, and the goal is to compute a minimum-cost ride satisfying all requests. This ride sharing problem is shown to be tractable on paths by designing a $O(h \log h+n)$ algorithm, with $h$ being the number of distinct requests and with $n$ being the number of nodes in the path. The algorithm is then used as a subroutine to efficiently solve instances defined over cycles, hence covering all graphs with maximum degree $2$. This traces the frontier of tractability, since $\bf NP$-hard instances are exhibited over trees whose maximum degree is $3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
