In the \textsc{Waypoint Routing Problem} one is given an undirected capacitated and weighted graph $G$, a source-destination pair $s,t\in V(G)$ and a set $W\subseteq V(G)$, of \emph{waypoints}. The task is to find a walk which starts at the source vertex $s$, visits, in any order, all waypoints, ends at the destination vertex $t$, respects edge capacities, that is, traverses each edge at most as many times as is its capacity, and minimizes the cost computed as the sum of costs of traversed edges with multiplicities. We study the problem for graphs of bounded treewidth and present a new algorithm for the problem working in $2^{O(\mathrm{tw})}\cdot n$ time, significantly improving upon the previously known algorithms. We also show that this running time is optimal for the problem under Exponential Time Hypothesis.
翻译：在 \ textsc{ waypoint Routing problem} 中, 给一个没有方向的电动和加权的图形$G$, 一个源- 目的地对一对美元, t\ in V( G)$, 和一套 $W\ subseteq V( G)$, 也就是 emph{ waypoints} 。 任务在于找到一个从源顶点$ 开始的行走, 访问, 任何顺序, 所有途径点, 终点在目的地的顶点 $t, 尊重边缘能力, 也就是, 每个边缘的跨度最多与其容量一样多的倍, 并尽可能降低以多功能的跨度边缘成本总和计算的成本。 我们研究了 $O (\ mathrm{ tw}\ cdodotodat n$) 的问题, 并在 2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
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