Streaming and Query Once Space Complexity of Longest Increasing Subsequence

Longest Increasing Subsequence ( \(\textsf {LIS}\) ) 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 \(\textsf {LIS}\) , yet only a few on the equally important space complexity. In this paper, we further study the space complexity of computing and approximating \(\textsf {LIS}\) 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 \(\textsf {LIS}\) in these models. Besides the bounds, our work also leaves many intriguing open problems.