低次格空间
Lattice spanners of low degree
摘要：
设$δ_0(P,k)$表示平面几何空间域上点集$P$的度$k$膨胀。若$Λ$是无限正方形点阵，则证明了$1+\sqrt{2} \leq δ_0(Λ,3) \leq (3+2\sqrt2) \, 5^{-1/2} = 2.6065\ldots$和$δ_0(Λ,4) = \sqrt{2}$ .当$Λ$为无限六方点阵时，证明了$δ_0(Λ,3) = 1+\sqrt{3}$和$δ_0(Λ,4) = 2$ .我们所有的构造都是限制在度$3$或$4$的平面格点镶嵌。
英文摘要：
Let $δ_0(P,k)$ denote the degree $k$ dilation of a point set $P$ in the domain of plane geometric spanners. If $Λ$ is the infinite square lattice, it is shown that $1+\sqrt{2} \leq δ_0(Λ,3) \leq (3+2\sqrt2) \, 5^{-1/2} = 2.6065\ldots$ and $δ_0(Λ,4) = \sqrt{2}$. If $Λ$ is the infinite hexagonal lattice, it is shown that $δ_0(Λ,3) = 1+\sqrt{3}$ and $δ_0(Λ,4) = 2$. All our constructions are planar lattice tilings constrained to degree $3$ or $4$.
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。
