The evolving data framework was first proposed by Anagnostopoulos et al., where an evolver makes small changes to a structure behind the scenes. Instead of taking a single input and producing a single output, an algorithm judiciously probes the current state of the structure and attempts to continuously maintain a sketch of the structure that is as close as possible to its actual state. There have been a number of problems that have been studied in the evolving framework including our own work on labeled trees. We were motivated by the problem of maintaining a labeling in the plane, where updating the labels require physically moving them. Applications involve tracking evolving disease hot-spots via mobile testing units , and tracking unmanned aerial vehicles. To be specific, we consider the problem of tracking labeled nodes in the plane, where an evolver continuously swaps labels of any two nearby nodes in the background unknown to us. We are tasked with maintaining a hypothesis, an approximate sketch of the locations of these labels, which we can only update by physically moving them over a sparse graph. We assume the existence of an Oracle, which when suitably probed, guides us in fixing our hypothesis.

翻译：演化数据框架最早由Anagnostopoulos等人提出，其中演化器会在后台对结构进行微小改动。算法并非接收单一输入并产生单一输出，而是通过审慎探测结构的当前状态，持续维护尽可能接近真实状态的结构草图。在该演化框架中已有多个问题得到研究，包括我们在带标签树上的工作。我们受平面中标签维护问题的启发——在此场景中，更新标签需要物理移动它们。相关应用包括通过移动检测单元追踪演化中的疾病热点，以及追踪无人机。具体而言，我们研究平面中有标签节点的追踪问题：演化器在后台持续交换任意两个邻近节点的标签（此过程对我们不可见）。我们的任务是维护一个"假设"——即对这些标签位置的近似草图，只能通过在稀疏图上物理移动节点来更新。我们假设存在一个预言机，在适当探测后，它能指导我们修正该假设。