The techniques developed in the paper for handling small LIS queries can potentially be extended to solve other variants of the LIS problem, such as the dynamic LIS problem or the streaming LIS problem.
For the dynamic LIS problem, where the goal is to maintain the length of the LIS under insertion and deletion of elements, the first technique discussed in the paper could be adapted. By updating the precomputed data structures efficiently upon each insertion or deletion, it may be possible to maintain the LIS information dynamically. This could involve modifying the data structures and algorithms to handle changes in the sequence in an incremental or decremental manner.
Similarly, for the streaming LIS problem, where computing the LIS requires limited space and involves processing elements in a streaming fashion, the techniques developed in the paper could be useful. By incorporating concepts of approximation algorithms and efficient data structures, it may be feasible to approximate the LIS in a streaming setting while maintaining low space complexity.
Overall, the underlying principles of precomputation, dynamic updates, and efficient data structures can be leveraged to address the dynamic and streaming variants of the LIS problem.