论文信息 - On Some Largest Empty Orthoconvex Polygons in a Point Set

On Some Largest Empty Orthoconvex Polygons in a Point Set

Efficient algorithms for finding some largest empty ortho convex polygons in a point set are presented in this paper. This class of problems are generalizations of the maximum empty rectangle problem. We present simple and efficient algorithms for finding the largest empty ortho convex polygons of the following classes. The algorithm for the L (which is the simplest isothetic polygon after a rectangle) runs in O(n2logn) time in the expected case and O(n3) time in worst case. The algorithms for the cross shaped polygon, the point visible ortho convex polygon and line visible ortho convex polygon run in O(n3) time. Finally, the algorithm for the edge visible ortho convex polygon runs in O(n2) time.

Amitava Datta | G. D. S. Ramkumar

[1] Alok Aggarwal,et al. Geometric applications of a matrix-searching algorithm , 1987, SCG '86.

[2] Bernard Chazelle,et al. Computing the Largest Empty Rectangle , 1986, SIAM J. Comput..

[3] J. O'Rourke. Art gallery theorems and algorithms , 1987 .

[4] Alok Aggarwal,et al. Fast algorithms for computing the largest empty rectangle , 1987, SCG '87.

[5] Derick Wood,et al. Ortho-Convexity and its Generalizations , 1988 .

[6] Michael Ian Shamos,et al. Computational geometry: an introduction , 1985 .

[7] D. T. Lee,et al. On the maximum empty rectangle problem , 1984, Discret. Appl. Math..

[8] Leonidas J. Guibas,et al. Finding extremal polygons , 1982, STOC '82.

[9] Chee-Keng Yap,et al. A Polynomial Solution for Potato-peeling and other Polygon Inclusion and Enclosure Problems , 1984, FOCS.

[10] Derick Wood,et al. On Rectangular Visibility , 1988, J. Algorithms.

[11] Derick Wood,et al. An Isothetic View of Computational Geometry† †Work carried out under a Natural Sciences and Engineering Research Council of Canada Grant No. A-5692. , 1985 .