具有不经意异步机器人的最优确定性环探索
Optimal deterministic ring exploration with oblivious asynchronous robots
摘要：
我们考虑的问题，探索一个匿名的无方向环的大小$n$由$k$相同的，不经意的，异步的移动机器人，是无法通信，但有能力感知他们的环境，并根据他们的本地视图作出决定。以前的作品在这个弱的情况下证明，$k$必须不分$n$的确定性解决方案存在。此外，已知探索大小为$n$的环的机器人的最小数量（确定性的或概率性的）是4。在确定性的情况下，17个机器人的上限成立，而4个概率机器人是足够的。在本文中，我们关闭的复杂性的差距，在确定性的设置，通过证明，没有确定性的探索是可行的，只要小于5个机器人的大小的环是偶数，和5个机器人是足够的任何$n$是互质的五个。我们的协议在O（n）机器人移动中完成探索，这也是最优的。
英文摘要：
We consider the problem of exploring an anonymous unoriented ring of size $n$ by $k$ identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that $k$ must not divide $n$ for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size $n$ is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots whenever the size of the ring is even, and that five robots are sufficient for any $n$ that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.
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。
