图的辫群计算及其在机器人运动规划中的应用
Computing braid groups of graphs with applications to robot motion planning
摘要：
我们设计了一个算法，写下图辫群的表示。发电机表示的实际运动的机器人移动没有碰撞在一个给定的图形。一个关键因素是一个新的运动规划算法，其复杂性是线性的边缘和机器人的数量平方。该算法表明所有轻可平面图的2-点辫群都有关系子是交换子的表示。
英文摘要：
We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph. A key ingredient is a new motion planning algorithm whose complexity is linear in the number of edges and quadratic in the number of robots. The computing algorithm implies that 2-point braid groups of all light planar graphs have presentations where all relators are commutators.
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。
