Geometric applications of a matrix-searching algorithm

@article{Aggarwal1986GeometricAO,
  title={Geometric applications of a matrix-searching algorithm},
  author={A. Aggarwal and M. Klawe and S. Moran and P. 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… Expand
364 Citations
Selection in Monotone Matrices and Computing kth Nearest Neighbors
  • 4
An efficient algorithm for row minima computations in monotone matrices
  • K. Nakano, S. Olariu
  • Computer Science
  • Proceedings of the 1996 ICPP Workshop on Challenges for Parallel Processing
  • 1996
Superlinear Bounds for Matrix Searching Problems
  • M. Klawe
  • Mathematics, Computer Science
  • J. Algorithms
  • 1992
  • 15
Selection and sorting in totally monotone arrays
  • 13
  • PDF
Improved Selection on Totally Monotone Arrays
  • 1
  • PDF
An Eecient Algorithm for Row Minima Computations on Basic Reconngurable Meshes
  • Koji Nakanoy, Stephan Olariuz
  • 1998
Applications of generalized matrix searching to geometric algorithms
  • 45
...
1
2
3
4
5
...

References

SHOWING 1-2 OF 2 REFERENCES
Finding extremal polygons
  • 53
  • Highly Influential
The All Nearest-Neighbor Problem for Convex Polygons
  • 38
  • Highly Influential