Recently, Armstrong, Guzm\'an, and Sing Long (2021), presented an optimal $O(n^2)$ time algorithm for strict circular seriation (called also the recognition of strict quasi-circular Robinson spaces). In this paper, we give a very simple $O(n\log n)$ time algorithm for computing a compatible circular order for strict circular seriation. When the input space is not known to be strict quasi-circular Robinson, our algorithm is complemented by an $O(n^2)$ time verification of compatibility of the returned order. This algorithm also works for recognition of other types of strict circular Robinson spaces known in the literature. We also prove that the circular Robinson dissimilarities (which are defined by the existence of compatible orders on one of the two arcs between each pair of points) are exactly the pre-circular Robinson dissimilarities (which are defined by a four-point condition).

翻译：最近，Armstrong、Guzmán和Sing Long（2021）提出了一个最优的$O(n^2)$时间复杂度的严格循环排序算法（也称为严格拟循环Robinson空间的识别）。本文给出了一种极其简单的$O(n\log n)$时间复杂度的算法，用于计算严格循环排序的相容循环顺序。当输入空间尚未被确认为严格拟循环Robinson时，我们的算法辅以$O(n^2)$时间复杂度的相容性验证过程，以检验返回顺序的有效性。该算法同样适用于文献中其他类型的严格循环Robinson空间的识别。此外，我们证明了循环Robinson相异性（定义为每对点之间的两段弧中至少存在一段弧上的相容顺序）恰好是前循环Robinson相异性（定义为满足四点条件）。