Geometric applications of a matrix-searching algorithm

@article{Aggarwal1986GeometricAO,
  title={Geometric applications of a matrix-searching algorithm},
  author={Alok Aggarwal and Maria M. Klawe and Shlomo Moran and Peter W. Shor and Robert E. Wilber},
  journal={Algorithmica},
  year={1986},
  volume={2},
  pages={195-208}
}
LetA be a matrix with real entries and letj(i) be the index of the leftmost column containing the maximum value in rowi ofA.A is said to bemonotone ifi1 >i2 implies thatj(i1) ≥J(i2).A istotally monotone if all of its submatrices are monotone. We show that finding the maximum entry in each row of an arbitraryn xm monotone matrix requires Θ(m logn) time, whereas if the matrix is totally monotone the time is Θ(m) whenm≥n and is Θ(m(1 + log(n/m))) whenm<n. The problem of finding the maximum value… 
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