The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Computational geometry: an introduction
Computational geometry: an introduction
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Pattern Recognition Letters
The Largest Empty Annulus Problem
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Dynamically Maintaining the Widest k -Dense Corridor
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Smallest k-point enclosing rectangle and square of arbitrary orientation
Information Processing Letters
On finding a widest empty 1-corner corridor
Information Processing Letters
Improved Algorithm for a Widest 1-Corner Corridor
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Improved algorithm for the widest empty 1-corner corridor
Information Processing Letters
Locating an Obnoxious Line among Planar Objects
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Smallest k-point enclosing rectangle and square of arbitrary orientation
Information Processing Letters
On finding a widest empty 1-corner corridor
Information Processing Letters
Recognition of minimum width color-spanning corridor and minimum area color-spanning rectangle
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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A k-dense corridor through a finite set, S, of n points in the plane is the open region of the plane that is bounded by two parallel lines that intersect the convex hull of S and such that the region contains k points of S. The problem of finding a widest k-dense corridor arises in robot motion-planning. In this paper, efficient solutions are presented for several versions of this problem. Results include: two algorithms for finding widest k-dense corridors for any k, an algorithm to dynamically maintain a widest empty corridor under online insertions and deletions in S, an algorithm to find a widest (n - 1)-dense closed corridor, and a widest empty corridor algorithm for polygonal obstacles. The techniques used are based on geometric duality and on efficient searching in the convex layers of a point-set.