The complexity class CLS was proposed by Daskalakis and Papadimitriou in 2011 to understand the complexity of important NP search problems that admit both path following and potential optimizing algorithms. Here we identify a subclass of CLS – called UniqueEOPL – that applies a more specific combinatorial principle that guarantees unique solutions. We show that UniqueEOPL contains several important problems such as the P-matrix Linear Complementarity Problem, finding fixed points of Contraction Maps, and solving Unique Sink Orientations (USOs). We identify a problem – closely related to solving contraction maps and USOs – that is complete for UniqueEOPL.

复杂度类CLS由Daskalakis和Papadimitriou于2011年提出，旨在理解重要的NP搜索问题的复杂性，这些问题既包含路径跟踪也包括潜在的优化算法。在这里，我们确定了CLS的子类-称为UniqueEOPL-应用了更具体的组合原则来保证独特的解决方案。我们表明，UniqueEOPL包含几个重要问题，例如P矩阵线性互补问题，找到收缩图的固定点以及解决唯一下沉方向（USO）。我们确定一个与解决收缩图和USO紧密相关的问题，这对于UniqueEOPL是完整的。