Improved Algorithm for a Widest 1-Corner Corridor

Given a set P of n points on a 2D plane, the 1-corner empty corridor is a region inside the convex hull of P which is bounded by a pair of links; each link is an unbounded trapezium bounded by two parallel half-lines, and it does not contain any point of P . We present an improved algorithm for computing the widest empty 1-corner corridor that runs in O (n 3log2 n ) time and O (n 2) space. This improves the time complexity of the best known algorithm for the same problem by a factor of $\frac{n}{\log n}$[4].

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