(Data) STRUCTURES

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: (a) high-dimensional problems, where the goal is to show large space lower bounds; (b) constant-dimensional geometric problems, where the goal is to bound the query time for space O(n polylg n); (c) 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 lglg n factor.) Our reductions also imply the following new results: (a) an Omega(lg n / lg lg n) bound for 4-dimensional range reporting, given space O(n ldr poly lg n). This is very timely, since a recent result [Nekrich, SoCG'07] solved 3D reporting in near-constant time, raising the prospect that higher dimensions could also be easy; (b) a tight space lower bound for the partial match problem, for constant query time.(c) the first lower bound for reachability oracles.