周边监视问题的进展
Progress on a perimeter surveillance problem
摘要：
我们考虑由Kingston，Beard和Holt在2008年提出的周界监视问题，并由Davis，Humphrey和Kingston在2019年研究。在这个问题中，$n$无人机在有限的时间间隔内进行监视，以匀速移动，只有在遇到另一架无人机时才交换信息。Kingston等人描述了一种特殊的在线算法来协调它们的行为，并询问了在无人机完全同步之前需要多长时间的上限。他们将算法的行为分为两个阶段，并根据最坏情况的配置给出了每个阶段长度的上限。戴维斯等人提出了第一阶段猜想的反例。我们提出了尖锐的上界第2阶段，这表明在这种情况下，最坏的情况是正确的。我们还提出了新的下限第1阶段和总时间同步，并报告部分进展取得了上限。
英文摘要：
We consider a perimeter surveillance problem introduced by Kingston, Beard, and Holt in 2008 and studied by Davis, Humphrey, and Kingston in 2019. In this problem, $n$ drones surveil a finite interval, moving at uniform speed and exchanging information only when they meet another drone. Kingston et al. described a particular online algorithm for coordinating their behavior and asked for an upper bound on how long it can take before the drones are fully synchronized. They divided the algorithm's behavior into two phases, and presented upper bounds on the length of each phase based on conjectured worst-case configurations. Davis et al. presented counterexamples to the conjecture for phase 1. We present sharp upper bounds on phase 2 which show that in this case the conjectured worst case is correct. We also present new lower bounds on phase 1 and the total time to synchronization, and report partial progress towards obtaining an upper bound.
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