Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search

  title={Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search},
  author={Pawel Gawrychowski and Shay Mozes and Oren Weimann},
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… 
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