A Robinson space is a dissimilarity space $(X,d)$ (i.e., a set $X$ of size $n$ and a dissimilarity $d$ on $X$) for which there exists a total order $<$ on $X$ such that $x<y<z$ implies that $d(x,z)\ge \max\{ d(x,y), d(y,z)\}$. Recognizing if a dissimilarity space is Robinson has numerous applications in seriation and classification. An mmodule of $(X,d)$ (generalizing the notion of a module in graph theory) is a subset $M$ of $X$ which is not distinguishable from the outside of $M$, i.e., the distance from any point of $X\setminus M$ to all points of $M$ is the same. If $p$ is any point of $X$, then $\{ p\}$ and the maximal by inclusion mmodules of $(X,d)$ not containing $p$ define a partition of $X$, called the copoint partition. In this paper, we investigate the structure of mmodules in Robinson spaces and use it and the copoint partition to design a simple and practical divide-and-conquer algorithm for recognition of Robinson spaces in optimal $O(n^2)$ time.

翻译：罗宾逊空间是一种相异空间 $(X,d)$（即一个大小为 $n$ 的集合 $X$ 及其上的相异度量 $d$），其中存在一个全序 $<$ 使得若 $x<y<z$，则 $d(x,z)\ge \max\{ d(x,y), d(y,z)\}$。识别相异空间是否为罗宾逊空间在排序和分类中具有广泛应用。$(X,d)$ 的一个 m模块（推广了图论中模块的概念）是 $X$ 的子集 $M$，其外部不可区分，即对于任意 $X\setminus M$ 中的点，到 $M$ 中所有点的距离均相同。若 $p$ 是 $X$ 中任意一点，则 $\{ p\}$ 与 $(X,d)$ 中不包含 $p$ 的极大（按包含关系）m模块构成 $X$ 的一个划分，称为余点划分。本文研究罗宾逊空间中 m模块的结构，并利用该结构及余点划分设计了一种简单实用的分治算法，可在最优的 $O(n^2)$ 时间内完成罗宾逊空间的识别。