We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. The existence of such embedding enables a reduction from the version of the matroid secretary problem where the matroid is unknown to the version where the matroid is known in advance. We show that online matroid embeddings exist for binary (and hence graphic) and laminar matroids. We also show a negative result showing that no online matroid embedding exists for the class of all matroids. Finally, we define the notion of an approximate matroid embedding, generalizing the notion of {\alpha}-partition property, and provide an upper bound on the approximability of binary matroids by a partition matroid, matching the lower bound of Dughmi et al.

翻译：本文引入了在线拟阵嵌入的概念，这是一种将在线方式逐步揭示的未知拟阵映射到已知的更大拟阵的算法。此类嵌入的存在使得可以将拟阵未知情形下的秘书问题归约至拟阵预先已知的情形。我们证明了在线拟阵嵌入在二元拟阵（从而包括图拟阵）与层状拟阵中存在。同时，我们给出了一个否定性结果，表明对于所有拟阵构成的类不存在在线拟阵嵌入。最后，我们定义了近似拟阵嵌入的概念，推广了{\alpha}-划分性质的定义，并给出了二元拟阵通过划分拟阵进行近似的可逼近性上界，该结果与Dughmi等人提出的下界相匹配。