Covering a polygonal region by rectangles
Covering a polygonal region by rectangles
复制标题
用矩形覆盖多边形区域
DOI：
--
复制
发表时间：
2011
影响因子：
2.2
通讯作者：
A. Krivulya
中科院分区：
文献类型：
--
作者：
Y. Stoyan;T. Romanova;G. Scheithauer;A. Krivulya
考虑用有限的矩形族覆盖紧凑的多边形区域（称为目标区域）的问题。提供了对问题进行数学建模的工具。特别是，引入了称为 Γ 函数的函数，该函数指示矩形相对于其配置是否形成目标区域的覆盖。 Γ 函数的构造与 Φ 函数的构造类似，后者已被证明是解决打包问题的有效工具。提出了基于Γ函数的覆盖问题的数学模型以及求解策略。通过一个例子说明了该方法并给出了一些计算结果。
The problem of covering a compact polygonal region, called target region, with a finite family of rectangles is considered. Tools for mathematical modeling of the problem are provided. Especially, a function, called Γ-function, is introduced which indicates whether the rectangles with respect to their configuration form a cover of the target region or not. The construction of the Γ-function is similar to that of Φ-functions which have been proved to be an efficient tool for packing problems. A mathematical model of the covering problem based on the Γ-function is proposed as well as a solution strategy. The approach is illustrated by an example and some computational results are presented.