A good submatrix is hard to find

Authors:
John J. Bartholdi, III
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
Venue:
Operations Research Letters
Year:
1982

Citing 2
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Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

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Abstract

Given a matrix, it is NP-hard to find a 'large' column, row, or arbitraty submatrix that satisfies property @p, where @p is nontrivial, holds for permutation matrices, and is hereditary on submatrices. Such properties include totally unimodular, transformable to a network matrix, permutable to consecutive ones, and many others. Similar results hold for properties such as positive definite, of bandwidth w, and symmetric.