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Volume Maximization and Orthoconvex Aproximation of Orthogons

机译:正交的体积最大化和正交凸近似

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Let n axes-parallel hyperparallelepipeds (also called blocks) of the d-dimensional Euclidean space and a positive integer r be given. The volume maximization problem (VMP) selects at most r blocks such that the volume of their union becomes maximum. VMP is shown tobe ND -hard in the 2-dimensional case and polynomially solvable for the line via a constrained critical path problem (CCPP) in an acyclic digraph. This CCPP leads to further well solvable special cases of the maximization problem. In particular, the following approximation problem (OAP) becomes polynomially solvable given an orthogon p (i.e,a simple polygon in the plane which is a union of blocks) and a positive integer q, find an orthoconvex orthogon with at most q vertices and minimum area, which contains P.
机译:给出d维欧氏空间的n个轴平行超平行六面体(也称为块)和一个正整数r。体积最大化问题(VMP)最多选择r个块,以使它们的并集的体积变为最大。 VMP在二维情况下显示为ND困难,并且可以通过无环有向图中的约束关键路径问题(CCPP)对线进行多项式求解。此CCPP导致最大化问题的进一步可解决的特殊情况。特别是,给定一个正交数p(即一个平面的简单多边形,它是一个块的并集)和一个正整数q,下面的逼近问题(OAP)可以通过多项式求解,找到一个最多具有q个顶点且最小的正凸正交多边形包含P的区域。

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