Talk: Cell-Probe Lower Bounds from Online Communication Complexity

Abstract: In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players Bob his input piece-by-piece, and has the players Alice and Bob cooperate to compute a result it presents Bob with the next piece. This model has a closer and more natural correspondence to dynamic data structures than the classic communication models do and hence presents a new perspective on data structures.

We first present a lower bound for the online set intersection problem in the online communication model, demonstrating a general approach for proving online communication lower bounds. The online communication model prevents a batching trick that classic communication complexity allows, and yields a stronger lower bound. Then we apply the online communication model to data structure lower bounds by studying the Group Range Problem, a dynamic data structure problem. This problem admits an O(log n)-time worst-case data structure. Using online communication complexity, we prove a tight cell-probe lower bound: spending o(log n) (even amortized) time per operation results in at best an exp(-\delta^2 n) probability of correctly answering a (1/2 + \delta)-fraction of the n queries.

Joint work with Joshua Wang and Huacheng Yu.