In this work, we extend the concept of Robinson spaces to asymmetric dissimilarities, enhancing their applicability in representing and analyzing complex data. Within this generalized framework, we introduce two different problems that extend the classical seriation problem: an optimization problem and a decision problem. We establish that these problems are NP-hard and NP-complete, respectively. Despite this complexity results, we identify several non-trivial instances where these problems can be solved in polynomial time, providing valuable insights into their tractability.

翻译：本研究将Robinson空间的概念推广至非对称相异性度量，增强了其在复杂数据表示与分析中的适用性。在此广义框架下，我们提出了两个拓展经典排序问题的新问题：一个优化问题与一个判定问题。我们证明了这两个问题分别属于NP-hard和NP-complete问题。尽管存在这样的复杂性结论，我们仍发现了若干非平凡实例，可在多项式时间内求解这些问题，这为理解其可计算性提供了重要见解。