Widest-corridor Problems

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. ACM CCS