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,阿姆斯特朗、Guzm\'an和Sing Long(2021年)提出了一个用于严格循环演练(也称为承认严格的准循环罗宾逊空间)的最佳时间算法。 在本文中,我们给出了一个非常简单的美元(n\log n)时间算法,用于计算一个兼容的循环演练命令。当输入空间不为严格的准循环 Robinson所知时,我们的算法就得到一个美元(n2)美元(n2)对返回命令兼容性的时间核查的补充。这个算法还有助于识别文献中已知的其他类型的严格循环罗宾逊空间。 我们还证明,罗宾逊圆的不相似性(其定义是每对两对角之间两弧线之一的兼容性命令的存在)正是 Robinson 之前的不相似性(由四点条件定义 ) 。