Let $G$ be a non-trivial simple graph with vertices $V\left(G\right)=V$ and edges $E\left(G\right)=E$, and let $n=\left|V\right|,m=\left|E\right|$. Computing the diameter of $G$ and the min–max center of $G$ ($\mathit{C}\left(G\right)$) are both quadratic-time ($O\left(m^2\right)$). A problem is strongly subquadratic-time if it is $O\left(m^{2-ϵ}\right)$ for some $ϵ>0$. If either the diameter problem or the center problem is strongly subquadratic-time, then the Strong Exponential Time Hypothesis would be violated. The same is true even for chordal graphs (graphs having no induced $n$-cycle for $n\ge 4$). This paper presents an algorithm that is faster than existing algorithms for the diameter problem for all chordal graphs.

With $\alpha \left(\mathit{C}\left(G\right)\right)$ the size of a largest independent vertex subset of $\mathit{C}\left(G\right)$, it is proven here that the diameter problem for chordal graphs is $O\left(\alpha \left(\mathit{C}\left(G\right)\right)m\right)$-time. The algorithm does not require knowledge of $\mathit{C}\left(G\right)$; nevertheless, it relates the diameter problem to the structure of $\mathit{C}\left(G\right)$.

Large-radius chordal graphs $G$ are likely to have small $\frac{\alpha \left(\mathit{C}\left(G\right)\right)}{\left|E\left(G\right)\right|}$, which suggests the existence of interesting classes of large-radius chordal graphs having strongly subquadratic-time diameter problems.

让 $G$ 是具有顶点的非平凡简单图 $V（G）=V$ 和边缘 $Ë（G）=Ë$， 然后让 $ñ=\left|V\right|，米=\left|Ë\right|$。计算直径$G$ 和的最小最大中心 $G$ （$\mathit{C}（G）$）都是二次时间（$Ø（{米}^2）$）。问题是强烈的次二次-时间，如果它是$Ø（{米}^{2-ϵ}）$ 对于一些 $ϵ>0$。如果直径问题或中心问题是强次时间，那么将违反强指数时间假说。即使对于弦图也是如此（没有归纳的图$ñ$-周期 $ñ\ge 4$）。针对所有弦图的直径问题，本文提出了一种比现有算法更快的算法。

和 $\alpha （\mathit{C}（G））$ 最大独立顶点子集的大小 $\mathit{C}（G）$，在这里证明弦图的直径问题是 $Ø（\alpha （\mathit{C}（G））米）$-时间。该算法不需要以下知识$\mathit{C}（G）$; 然而，它将直径问题与$\mathit{C}（G）$。

大半径弦图 $G$ 可能会很小 $\frac{\alpha （\mathit{C}（G））}{\left|Ë（G）\right|}$，这表明存在有趣的大半径弦图，它们具有强烈的次二次时间直径问题。