论文标题
有界树宽图上的航向路由
Waypoint Routing on Bounded Treewidth Graphs
论文作者
论文摘要
在\ textsc {Waypoint路由问题}中，给出了一个无向的电容和加权图$ g $，源污点对$ s，in v（g）$ in v（g）$和set $ w \ subseteq v（g）$，\ emph {waypoints}。任务是找到一条步行，从源顶点$ s $开始，按任何顺序访问，以所有路线的结尾，以目标顶点$ t $结束，尊重边缘能力，即最多多次穿越每个边缘，并将其最小化成本最小化，而成本最小化，而成本却是带有多重性的遍历成本的总和。我们研究了有界树宽的图的问题，并提出了一种新算法，用于$ 2^{o（\ mathrm {tw}）} \ cdot n $ time的问题，在先前已知的算法上有了显着改善。我们还表明，此运行时间对于指数时间假设下的问题是最佳的。
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.
