Abstract

We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: • high-dimensional problems, where the goal is to show large space lower bounds. • constant-dimensional geometric problems, where the goal is to bound the query time for space O(n·polylogn). • dynamic problems, where we are looking for a trade-off between query and update time. (In this case, our bounds are slightly weaker than the originals, losing a lglgn factor.) Our reductions also imply the following new results: • an Ω(lgn/lglgn) bound for 4-dimensional range reporting, given space O(n · polylogn). This is quite timely, since a recent result [39] solved 3D reporting in O(lg 2 lgn) time, raising the prospect that higher dimensions could also be easy. • a tight space lower bound for the partial match problem, for constant query time. • the first lower bound for reachability oracles. In the process, we prove optimal randomized lower bounds for lopsided set disjointness.

Citations