Computing Longest Increasing Subsequence Over Sequential Data Streams
  In this paper, we propose a data structure, a quadruple neighbor list (QN-list, for short), to support real time queries of all longest increasing subsequence (LIS) and LIS with constraints over sequential data streams. The QN-List built by our algorithm requires $O(w)$ space, where $w$ is the time window size. The running time for building the initial QN-List takes $O(w\log w)$ time. Applying the QN-List, insertion of the new item takes $O(\log w)$ time and deletion of the first item takes $O(w)$ time. To the best of our knowledge, this is the first work to support both LIS enumeration and LIS with constraints computation by using a single uniform data structure for real time sequential data streams. Our method outperforms the state-of-the-art methods in both time and space cost, not only theoretically, but also empirically. 
Youhuan Li, Lei Zou, Huaming Zhang, Dongyan Zhao
cs.DS