  Longest Increasing Subsequence (LIS) is a fundamental problem in
combinatorics and computer science. Previously, there have been numerous works
on both upper bounds and lower bounds of the time complexity of computing and
approximating LIS, yet only a few on the equally important space complexity.
  In this paper, we further study the space complexity of computing and
approximating LIS in various models. Specifically, we prove non-trivial space
lower bounds in the following two models: (1) the adaptive query-once model or
read-once branching programs, and (2) the streaming model where the order of
streaming is different from the natural order.
  As far as we know, there are no previous works on the space complexity of LIS
in these models. Besides the bounds, our work also leaves many intriguing open
problems.
