Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed using an equilateral triangle, a square, or a regular hexagon. However, all other shapes have remained elusive. In this paper we extend the restricted class of spanners for which tight bounds are known. We prove that Delaunay triangulations constructed using rectangles with aspect ratio $\A$ have spanning ratio at most $\sqrt{2} \sqrt{1+\A^2 + \A \sqrt{\A^2 + 1}}$, which matches the known lower bound.

翻译：Spanner 构造是一个研究周密的问题, Delaunay 三角匹配是最受欢迎的捕捉者之一。 如果Delaunay 三角匹配是用等边三角、 方形或普通六边形构建的, 则已知的界线很紧。 然而, 所有其他形状仍然难以找到 。 在本文中, 我们扩展了已知有紧身界限的受限的打手类别 。 我们证明, 使用 $\ A$ 的 矩形构造的Delaunay 三角匹配的宽幅比例最高为$\ sqrt{2}\ sqrt{1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ + 1\ $, 这与已知的下边框相符 。