The isomorphic version of Brualdies nestedness is in P

@inproceedings{Berger2016TheIV,
  title={The isomorphic version of Brualdies nestedness is in P},
  author={Annabell Berger},
  year={2016}
}
  • A. Berger
  • Published 8 February 2016
  • Mathematics
The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson 1998 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… 

(0, 1)-Matrices, Discrepancy and Preservers

Let m and n be positive integers, and let R = (r1, . . . , rm) and S = (s1, . . . , sn) be nonnegative integral vectors. Let A(R,S) be the set of all m × n (0, 1)-matrices with row sum vector R and

Decompose Boolean Matrices with Correlation Clustering

This paper presents a method based on the similarity of rows and columns, which uses correlation clustering to cluster the rows and Columns of the matrix, facilitating the visualization of the relation by rearranging therows and columns.

References

SHOWING 1-8 OF 8 REFERENCES

Computing the Minimum Fill-in is NP^Complete

We show that the following problem is NP-complete. Given a graph, find the minimum number of edges (fill-in) whose addition makes the graph chordal. This problem arises in the solution of sparse

Combinatorial Matrix Classes

1. Introduction 2. Basic existence theorems for matrices with prescribed properties 3. The class A(R S) of (0,1)-matrices 4. More on the class A(R S) of (0,1)-matrices 5. The class T(R) of tournament

Nested species subsets, gaps, and discrepancy

This work revisits previous analyses of nested faunas and introduces a new metric the authors call “discrepancy” which is recommended as a measure for nestedness and recommends that the sample spaces conserve both row sums and column sums derived from the incidence matrix.

A consumer's guide to nestedness analysis

It is observed that traditional ‘gap-counting’ metrics are biased towards species loss among columns (occupied sites) and that many metrics are not invariant to basic matrix properties and that the study of nestedness should be combined with an appropriate gradient analysis to infer possible causes of the observed presence absence sequence.

Discrepancy of Matrices of Zeros and Ones

The minimum discrepancy problem is completely solved by giving an explicit formula in terms of $R$ and $S$ for it and an algorithm to compute the maximum discrepancy is found.

Implementation of algorithms for maximum matching on nonbipartite graph, dissertation

  • 1974

Patterns in permuted binary matrices, dissertation

  • Threshold graphs and related topics
  • 1995