Geodesic Spanners for Points in $\mathbb{R}^3$ amid Axis-parallel Boxes

几何相交图的稀疏有界跳生成子图

Sparse Bounded Hop-Spanners for Geometric Intersection Graphs

本文研究了多种几何相交图的2跳和3跳稀疏生成子图，给出了球、胖轴平行盒、半代数对象及四面体等图类的改进上界与下界。

Minimum-Link Shortest Paths for Polygons amidst Rectilinear Obstacles

Consider two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane such that the bounding boxes, one for each obstacle and one for each polygon, are disjoint. We present an algorithm that computes a minimum-link rectilinear shortest path connecting the two polygons in $O((N+n)\log (N+n))$ time using $O(N+n)$ space, where $n$ is the number of vertices in the domain and $N$ is the total number of vertices of the two polygons.

Resolution-Exact Planner for Thick Non-Crossing 2-Link Robots

We consider the path planning problem for a 2-link robot amidst polygonal obstacles. Our robot is parametrizable by the lengths $\ell_1, \ell_2>0$ of its two links, the thickness $τ\ge 0$ of the links, and an angle $κ$ that constrains the angle between the 2 links to be strictly greater than $κ$. The case $τ>0$ and $κ\ge 0$ corresponds to "thick non-crossing" robots. This results in a novel 4DOF configuration space ${\mathbb R}^2\times ({\mathbb T}\setminusΔ(κ))$ where ${\mathbb T}$ is the torus and $Δ(κ)$ the diagonal band of width $κ$. We design a resolution-exact planner for this robot usin…