1 research outputs found
Unifying the Landscape of Cell-Probe Lower Bounds
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 polylog n).
* 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:
* an Omega(lg n / lglg n) bound for 4-dimensional range reporting, given
space O(n polylog n). This is quite timely, since a recent result solved 3D
reporting in O(lglg n) 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.Comment: To appear in SIAM Journal on Computing (SICOMP). The conference
version appeared in FOCS'08 under the title "(Data) Structures