Improved Sublinear Time Algorithm for Longest Increasing Subsequence

Michael Mitzenmacher, Saeed Seddighin

Abstract: We present a novel sublinear time algorithm for approximating LIS. If we denote the ratio of the solution size over the input size by λ, our approach yields an algorithm with an approximation factor of Ω(λ∊) for any constant ∊ > 0, and a truly sublinear runtime. This improves over for example the recent work of Rubinstein et al. [RSSS19] that approximates LIS within a factor Ω(λ3) in truly sublinear time. Our work makes use of a grid packing technique recently introduced by Mitzenmacher and Seddighin to approximate LIS in the dynamic setting [MS20], providing another application for this technique.