We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(n log n/log log n)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms.

翻译：本文致力于解决在线/滑动模型中计算Lempel-Ziv因子分解最右变体的问题。此前，该问题的最佳已知复杂度为O(n log n)时间与O(n)空间，其中在线模型的结果由Amir等人[IPL 2002]提出，滑动模型的结果由Larsson[CPM 2014]提出。在本文中，我们针对在线/滑动两种模型，提出了更快的O(n log n/log log n)时间解决方案。我们的算法建立在一个名为BP-linked trees的简单数据结构，以及对动态整数列表上的范围最小/最大值查询（RmQ/RMQ）数据结构的一个轻微改进版本之上。我们还展示了我们算法的其他应用。