再论覆盖的八分体分解
More on Decomposing Coverings by Octants
摘要：
在本文中，我们通过证明空间中点集的每一个9重覆盖通过一个八分圆的三个平移分解为两个覆盖来改进我们前面给出的上界，并且通过构造一个不分解为两个覆盖的4重覆盖来改进我们的下界。同样的界限也适用于$\R^2$中的点被三角形的许多同素异义或平移所覆盖。我们还证明了某些动态区间着色问题等价于上述问题。
英文摘要：
In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. The same bounds also hold for coverings of points in $\R^2$ by finitely many homothets or translates of a triangle. We also prove that certain dynamic interval coloring problems are equivalent to the above question.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
