Covering polygons with minimum number of rectangles
- Cite this paper as:
- Lingas A. (1984) Covering polygons with minimum number of rectangles. In: Fontet M., Mehlhorn K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg
In the fabrication of masks for integrated circuits, it is desirable to replace the polygons comprising the layout of a circuit with as small as possible number of rectangles. Let Q be the set of all simple polygons with interior angles ≥ 90 degrees. Given a polygon P ε Q, let ϑ(P) be the minimum number of (possibly overlapping) rectangles lying within P necessary to cover P, and let r(P) be the ratio between the length of the longest edge of P and the length of the shortest edge of P. For every natural n ≥ 5, and k, a uniform polygon Pn,k with n corners is constructed such that r(Pn,k) ≥ k and ϑ(Pn) ≥ ω(nloglog(r(Pn,k))). On the other hand, by modifying a known heuristic it is shown that for all convex polygons P in Q with n vertices ϑ(P) ≤ O(nlog(r(P))).
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