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Full-Text Articles in Physical Sciences and Mathematics
There Is A Planar Graph Almost As Good As The Complete Graph, L Paul Chew
There Is A Planar Graph Almost As Good As The Complete Graph, L Paul Chew
Dartmouth Scholarship
Given a set S of points in the plane, there is a triangulation of S such that a path found within this triangulation has length bounded by a constant times the straight-line distance between the endpoints of the path. Specifically, for any two points a and b of S there is a path along edges of the triangulation with length less that sqrt(10) times [ab], where [ab] is the straight-line Euclidean distance between a and b. The triangulation that has this property is the L1 metric Delauney triangulation for the set S. This result can be applied to motion planning …
Computing The Largest Empty Rectangle, B. Chazelle, R. L. Drysdale, D. T. Lee
Computing The Largest Empty Rectangle, B. Chazelle, R. L. Drysdale, D. T. Lee
Dartmouth Scholarship
We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones …