Monge矩阵的子阵最大搜索等价于前序搜索
Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search
摘要：
本文提出了一种适用于n × n Monge矩阵子矩阵极大值查询的最优数据结构。我们的结果是一个双向的减少表明，这个问题是等价的经典的前任问题的多项式大小的宇宙。这给出了一个O（n）空间的数据结构，在O（loglogn）时间内回答子矩阵最大查询。它也给出了一个匹配的下界，表明O（loglogn）查询时间是最佳的任何数据结构的大小为O（n polylog（n））。我们的结果总结了一系列改进，这些改进始于SODA'12，查询时间为O（log^2 n），并在ICALP'14中继续进行，查询时间为O（log n）。最后，我们证明了部分Monge矩阵可以在与完整Monge矩阵相同的范围内处理。在前面的两个结果中，部分Monge矩阵引起了额外的逆Ackerman因子。
英文摘要：
We present an optimal data structure for submatrix maximum queries in n x n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(loglogn) time. It also gives a matching lower bound, showing that O(loglogn) query-time is optimal for any data structure of size O(n polylog(n)). Our result concludes a line of improvements that started in SODA'12 with O(log^2 n) query-time and continued in ICALP'14 with O(log n) query-time. Finally, we show that partial Monge matrices can be handled in the same bounds as full Monge matrices. In both previous results, partial Monge matrices incurred additional inverse-Ackerman factors.
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