凸多边形障碍物间路径规划的递归算法
A Recursive Algorithm for Routing amid Convex Polygonal Obstacles
浏览论文内容
中文总结 AI 辅助
本文针对含h个凸多边形障碍物的多边形域，提出一种递归路径规划算法，通过预处理生成路由表与标签，实现任意两点间带乘性拉伸比的路由。
中文摘要 AI 辅助
给定平面上由h个互不相交的凸多边形障碍物构成的多边形域𝒫，总顶点数为n，本文提出一种算法对𝒫进行预处理，以在𝒫的顶点上计算路由表，使得𝒫中任意顶点发出的数据包可路由至𝒫内的任意其他顶点。在数据包到达目的地前，沿路由路径的每个顶点v处，下一跳均通过v处的路由表及数据包头部存储的信息确定。预处理算法的时间复杂度为O(n²(lg n))，为𝒫的每个顶点分配大小为O(√h (lg h) lg n)的唯一标签，并在每个顶点计算大小为O(h lg n + √h(lg h)(min((1/ε)^O(lg α),n)) lg n)的路由表，输出的路由路径具有(7+ε)(lg h)的乘性拉伸比，其中ε>0为输入参数，α>1为几何参数。
英文摘要
Given a polygonal domain $\cal P$ comprising $h$ pairwise disjoint convex polygonal obstacles in the plane, together defined with $n$ vertices, this paper presents an algorithm to preprocess $\cal P$ to compute routing tables at the vertices of $\cal P$ so that a data packet from any vertex of $\cal P$ is routed to any other vertex belonging to $\cal P$. At every vertex $v$ of $\cal P$ along the routing path, until the packet reaches its destination, the next hop is determined using the routing tables at $v$ and the information stored in the packet header. In $O(n^2(\lg{n}))$ time, our preprocessing algorithm assigns a unique label of size $O(\sqrt{h} (\lg{h}) \lg{n})$ to each vertex of $\cal P$ and computes routing tables of size $O(h\lg{n} + \sqrt{h}(\lg{h})(\min((\frac{1}ε)^{O( \lg α)},n))$ $\lg {n})$ at each vertex of $\cal P$. The routing path output has a $(7 + ε)(\lg{h})$ multiplicative stretch. Here, $ε> 0$ is an input parameter and $α> 1$ is a geometric parameter.
