Cell-Probe lower bounds from online communication complexity

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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 each time before the next piece is revealed to Bob. This model has a closer and more natural correspondence to dynamic data structures than classic communication models do, and hence presents a new perspective on data structures. We first present a tight 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. We then apply the online communication model to prove data structure lower bounds for two dynamic data structure problems: the Group Range problem and the Dynamic Connectivity problem for forests. Both of the problems admit a worst case O(log n)-time data structure. Using online communication complexity, we prove a tight cell-probe lower bound for each: spending o(log n) (even amortized) time per operation results in at best an exp(− 2n) probability of correctly answering a (1/2 +)-fraction of the n queries.

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APA

Alman, J., Wang, J. R., & Yu, H. (2018). Cell-Probe lower bounds from online communication complexity. In Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 239–252). Association for Computing Machinery. https://doi.org/10.1145/3188745.3188862

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