用矩形覆盖多边形的算法

Q4 Mathematics
D.S. Franzblau, D.J. Kleitman
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引用次数: 51

摘要

多边形分解是计算几何中的一个基本问题,在模式识别和集成电路制造中有着广泛的应用。在这里,我们研究了用最小数量的矩形覆盖一个直线多边形(或多项式)的特殊情况,允许重叠。问题是NP-hard。然而,我们在这里给出了一个O(v2)算法来构造最小矩形覆盖,当多边形是垂直凸的。(这里v是顶点的数量。)该问题首先被简化为一维区间“基”问题。在证明我们的算法产生最优覆盖时,我们给出了最早由E. Györi (J. Combin Theory Ser.)证明的最小基-最大独立集对偶定理的一个新的证明。B 37, No. 1, 1 - 9)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An algorithm for covering polygons with rectangles

Decomposing a polygon into simple shapes is a basic problem in computational geometry, with applications in pattern recognition and integrated circuit manufacture. Here we examine the special case of covering a rectilinear polygon (or polyomino) with the minimum number of rectangles, with overlapping allowed. The problem is NP-hard. However, we give here an O(v2) algorithm for constructing a minimum rectangle cover, when the polygon is vertically convex. (Here v is the number of vertices.) The problem is first reduced to a 1-dimensional interval “basis” problem. In showing our algorithm produces an optimal cover we give a new proof of a minimum basis-maximum independent set duality theorem first proved by E. Györi (J. Combin Theory Ser. B 37, No. 1, 1–9).

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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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