周期变化图的探索
Exploration of Periodically Varying Graphs
摘要：
我们研究的可计算性和复杂性的探索问题在一类高度动态的图：周期性变化（PV）的图形，其中的边缘只存在于一些（未知）的时间定义的载体的周期性运动。这些图自然模型高度动态的基础设施少的网络，如公共交通与固定的时间表，低地球轨道（LEO）卫星系统，安全警卫的旅游等，我们建立必要的条件，解决问题。我们还推导出一般所需的时间量的下限，以及由限制类的运营商的运动定义的PV图：简单的路线，和循环路线。然后，我们证明，我们已经建立的可计算性和复杂性的限制确实是严格的。事实上，我们证明了所有必要条件也是充分的，所有的成本下界是紧的。我们这样做建设性地提出了两个最坏情况下的最优解算法，一个匿名系统，和那些不同的节点ID之一。一个额外的好处是算法相当简单。
英文摘要：
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. In fact we prove that all necessary conditions are also sufficient and all lower bounds on costs are tight. We do so constructively presenting two worst case optimal solution algorithms, one for anonymous systems, and one for those with distinct nodes ids. An added benefit is that the algorithms are rather simple.
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。
