Longest Increasing Subsequence Computation over Streaming Sequences

Youhuan Li, Lei Zou, Huaming Zhang, Dongyan Zhao

Abstract: 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 logw) time. Applying the QN-List, insertion of the new item takes O(logw) 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.