BARC/EADS Talk by Kasper Green Larsen
Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds
In this talk we prove the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.
We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a ∼Ω(lg1.5n) lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting over F2 ([Pat07]). Proving an ω(lgn) lower bound for this problem was explicitly posed as one of five important open problems in the late Mihai Patrascu's obituary [Tho13]. This result also implies the first ω(lgn) lower bound for the classical 2D range counting problem, one of the most fundamental data structure problems in computational geometry and spatial databases. We derive similar lower bounds for boolean versions of dynamic polynomial evaluation and 2D rectangle stabbing, and for the (non-boolean) problems of range selection and range median.
Our technical centerpiece is a new way of ``weakly" simulating dynamic data structures using efficient one-waycommunication protocols with small advantage over random guessing. This simulation involves a surprising excursion to low-degree (Chebychev) polynomials which may be of independent interest, and offers an entirely new algorithmic angle on the ``cell sampling" method of Panigrahy et al. [PTW10].
Kasper Green Larsen is an assistant professor at the Department of Computer Science at Aarhus University.
His research span in many areas of theoretical computer science, but in particular, he enjoys working on data structures, range searching, lower bounds, dimensionality reduction, and streaming algorithms.
Kasper received his Ph. D. from Aarhus University in 2013 and since 2017 he has been a member of the Young Academy under the Royal Danish Academy of Sciences and Letters.