Brualdies嵌套的同构版本是在P
The isomorphic version of Brualdies nestedness is in P
摘要：
来自Brualdi和Sanderson \cite{Brualdi1998}的$m \times n$ $0,1$ -矩阵的差异BR计算了$1$的最小数目，这些$1$需要在每行中向左移位以获得其费勒斯矩阵，即每行由连续的$1$和其后的连续的$0$组成.对于生态二分网络，BR描述了一组关系的嵌套程度。由于不同的标记矩阵可以是同构的，但具有不同的差异，我们定义了一个度量确定同构类中的最小差异。本文给出了$k\leq n$最小加权完美匹配问题的一个约化。
英文摘要：
The discrepancy BR for an $m \times n$ $0,1$-matrix from Brualdi and Sanderson \cite{Brualdi1998} counts the minimum number of $1$'s which need to be shifted in each row to the left to achieve its Ferrers matrix, i.e. each row consists of consecutive $1$'s followed by consecutive $0$'s. For ecological bipartite networks BR describes how nested a set of relationships is. Since different labeled matrices can be isomorphic but possess different discrepancies, we define a metric determining the minimum discrepancy in an isomorphic class. We give a reduction to $k\leq n$ minimum weighted perfect matching problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
