On Approximating the Corner Cover Problem
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چکیده
The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, one can consider covering the entire interior, the boundary and the set of corners of the polygon. These problems have important applications in, for example, storing images and in the manufacture of integrated circuits. In this paper we consider covering the corners of the polygons, also known as the corner-cover problem. In [4], it was shown that the corner cover problem is NP-hard and a simple O(n3=2)-time approximation algorithm with performance ratio of 4 was presented. In this paper, we propose a non-trivial heuristic that approximates the corner cover problem for rectilinear polygons without holes with an improved performance ratio of 2 of the optimum in O(n2) time. The analysis of the heuristic involves a very careful amortization scheme and we believe similar technique may be useful for analysis of heuristics for other geometric problems as well.
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تاریخ انتشار 1997