Computing Longest Increasing Subsequences over Sequential Data Streams

In this paper, we propose a unified index, an orthogonal list-based index, to support real time queries of all longest increasingsubsequence (LIS) and LIS with constraints over sequential datastreams. The index built by our algorithm requires O(w) space,where w is the time window size. The running time for building theinitial index takes O(wlogw) time. Applying the index, deletion ofthe first item takes O(w) time and insertion of the new item takesO(logw) time. To the best of our knowledge, this is the first work tosupport both LIS enumeration and constrained LIS computation byusing a single unified index for real time sequential data streams.Our method outperforms the state-of-the-art methods in both timeand space cost, not only theoretically, but also empirically.