  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.
