统一细胞探针下限的景观
Unifying the Landscape of Cell-Probe Lower Bounds
摘要：
我们发现，大部分的数据结构的下限今天已知的事实上遵循减少从通信复杂性的不平衡（不对称）集不相交。这包括下界：* 高维问题，目标是显示大空间下界。* 常维几何问题，其目标是将查询时间限制为空间O（n polylog n）。* 动态问题，我们正在寻找查询和更新时间之间的权衡。(In在这种情况下，我们的边界比原始边界稍弱，损失了lglg n因子。）我们的减少也意味着以下新的结果：* 一个欧米茄（lg n / lglg n）的4维范围报告，给定空间O（n polylog n）。这是非常及时的，因为最近的结果在O（lglg n）时间内解决了3D报告，提高了更高维度也很容易的前景。* 对于恒定的查询时间，部分匹配问题的紧空间下界。* 可达性预言的第一个下界。在这个过程中，我们证明了最佳的随机下界不平衡集不相交。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
