The isomorphic version of Brualdies nestedness is in P
Abstract
The discrepancy BR for an m × n 0,1-matrix from Brualdi and Sanderson 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≤ n minimum weighted perfect matching problems.
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