进化树上标签的最优跟踪
Optimally Tracking Labels on an Evolving Tree
摘要：
出于维护随着时间的推移而演变的大量点的数据结构的问题，我们考虑维护分配给树的顶点的一组标签的问题，其中这些标签的位置随着时间的推移而改变。我们研究的问题，在不断发展的数据框架，标签随着时间的推移而变化，由于一个代理的行动称为进化。该算法只能通过显式地探测树的各个节点来跟踪这些变化。该框架捕获了维护结构的最新视图的复杂性与使用可用视图计算的结果的质量之间的权衡。我们的研究结果允许数据的随机和对抗性演化，但允许算法和演化器之间的不同加速因子。我们表明，在极限，我们的算法保持标签的平均距离内的$O(1)$的实际位置。我们还提出了几乎匹配的下限。
英文摘要：
Motivated by the problem of maintaining data structures for a large sets of points that are evolving over the course of time, we consider the problem of maintaining a set of labels assigned to the vertices of a tree, where the locations of these labels change over time. We study the problem in the evolving data framework, where labels change over time due to the action of an agent called the evolver. The algorithm can only track these changes by explicitly probing individual nodes of the tree. This framework captures the tradeoff between the complexity of maintaining an up-to-date view of the structure and the quality of results computed with the available view. Our results allow for both randomized and adversarial evolution of the data, subject to allowing different speedup factors between the algorithm and the evolver. We show that in the limit, our algorithm maintains labels to within an average distance of $O(1)$ of their actual locations. We also present nearly matching lower bounds.
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