论文标题
两个机器人在树上移动地球
Two robots moving geodesically on a tree
论文作者
论文摘要
我们研究了$ \ ell_1 $和$ \ ell_2 $度量的订购和无序配置空间的地理复杂性。我们确定在$ \ ell_1 $和$ \ ell_1 $和$ \ ell_2 $指标中，任何星形图的订购两点$ \ varepsilon $ -Configuration空间的地球复杂性以及未订购的两点配置空间的$ \ ell_1 $中的任何树的未订购的两点配置空间，通过查找任何explicit geodels gecode explicit geodels gecodels gecode geodal geodal geodal geodal geodal goimal geodal geodal geodal geodal gode a，并将其配对编号。不断变化的家庭。在每种情况下，大地复杂性都与拓扑复杂性的已知值相匹配。
We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the $\ell_1$ and $\ell_2$ metrics. We determine the geodesic complexity of the ordered two-point $\varepsilon$-configuration space of any star graph in both the $\ell_1$ and $\ell_2$ metrics and of the unordered two-point configuration space of any tree in the $\ell_1$ metric, by finding explicit geodesics from any pair to any other pair, and arranging them into a minimal number of continuously-varying families. In each case the geodesic complexity matches the known value of the topological complexity.
