Covering a simple orthogonal polygon with a minimum number of orthogonally convex polygons

Authors:
R. A. Reckhow;J. Culberson
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1
Venue:
SCG '87 Proceedings of the third annual symposium on Computational geometry
Year:
1987

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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 &Ogr;(n2) algorithm for covering horizontally convex polygons is optimal, but can be improved to &Ogr;(n) for counting the number of polygons required for a minimal cover. We also give an optimal &Ogr;(n2) algorithm for covering 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.