有限通信距离的移动Agent疏散等边三角形
Evacuation of equilateral triangles by mobile agents of limited communication range
摘要：
我们考虑的问题疏散$k \geq 2$移动代理从一个单边等边三角形通过出口位于一个未知的位置上的周边的三角形。代理最初位于三角形的质心，并且它们可以与最多$r$和$0\leq r \leq 1$的距离处的其他代理通信。一个智能体最多可以以1的速度移动，并且只有当它到达出口所在的点时才能找到出口。特工们可以合作寻找出口。{ \em疏散问题}的目标是最小化疏散时间，定义为{ \em all}座席到达出口的最坏情况时间。我们提出并分析了几种算法的疏散问题的$k \geq 2$代理，我们的研究结果表明，要使用的最佳策略取决于$r$和$k$的值。对于两个代理，我们给出了三种算法，每一种算法都能在$0 \leq r \leq 1$范围内的$r$的不同子范围内实现最佳性能。最后，我们表明，对于任何$r$，疏散的$k=6 +2\lceil(\frac{1}{r}-1)\rceil$代理商可以在时间$1+\sqrt{3}/3$，这是最佳的时间，并渐近最佳的代理商的数量。
英文摘要：
We consider the problem of evacuating $k \geq 2$ mobile agents from a unit-sided equilateral triangle through an exit located at an unknown location on the perimeter of the triangle. The agents are initially located at the centroid of the triangle and they can communicate with other agents at distance at most $r$ with $0\leq r \leq 1$. An agent can move at speed at most one, and finds the exit only when it reaches the point where the exit is located. The agents can collaborate in the search for the exit. The goal of the {\em evacuation problem} is to minimize the evacuation time, defined as the worst-case time for {\em all} the agents to reach the exit. We propose and analyze several algorithms for the problem of evacuation by $k \geq 2$ agents; our results indicate that the best strategy to be used varies depending on the values of $r$ and $k$. For two agents, we give three algorithms, each of which achieves the best performance for different sub-ranges of $r$ in the range $0 \leq r \leq 1$. Finally, we show that for any $r$, evacuation of $k=6 +2\lceil(\frac{1}{r}-1)\rceil$ agents can be done in time $1+\sqrt{3}/3$, which is optimal in terms of time, and asymptotically optimal in terms of the number of agents.
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。
