Logarithmic Cell Probe Lower Bounds for Non-Deterministic Static Data Structures

In this paper, we present a new technique for proving static cell probe lower bounds. Our technique takes the field of static cell probe lower bounds one step further, by yielding the highest lower bound to date for any explicit problem, namely t = Ω((w− lg n)/ lg(S/n)), where w is the cell size in bits, n the input size, S the space of the data structure in number of cells, and t the cell probes needed to answer a query. Thus for linear space data structures we achieve t = Ω(lg n) when the cell size is just w ≥ (1 + ε) lg n for any constant ε > 0. Furthermore, our bounds also apply to non-deterministic static data structures, providing the first non-trivial lower bounds in the most natural setting of cell size w = Θ(lg n). Finally we believe our new technique sheds much new light on the seemingly inherent lower bound barrier of Ω(w), and we hope our results eventually may inspire ways of overcoming the barrier. ∗Kasper Green Larsen is a recipient of the Google Europe Fellowship in Search and Information Retrieval, and this research is also supported in part by this Google Fellowship. †Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation.