Abstract
The problem of covering a polygon with convex polygons has proven to be very difficult, even when restricted to the class of orthogonal polygons using orthogonally convex covers. We develop a method of analysis based on dent diagrams for orthogonal polygons and are able to show that Keil's O( n 2) algorithm for covering horizontally convex polygons is asymptotically optimal, but it can be improved to O( n) for counting the number of polygons required for a minimal cover. We also give an optimal O( n 2) covering algoring and an O( n ) counting algorithm for another subclass of orthogonal polygons. Finally, we develop a method of signatures which can be used to obtain polynomial time algorithms for an even larger class of orthogonal polygons.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have