Matrix sandwich problems

Martin Charles Golumbic

doi:10.1016/S0024-3795(97)10075-1

Matrix sandwich problems

Research output: Contribution to journal › Article › peer-review

Abstract

The Π Matrix Sandwich Problem (Π-MSP) is introduced here as follows: Given a {0, 1, *} valued matrix A, where * is interpreted as "do not care", does there exist a fill-in of the asterisks * with 0s and 1s such that the completed {0, 1} valued matrix M satisfies property Π? We study the computational complexity of this problem for several matrix properties including the Ferrers property, block decompositions and certain forbidden submatrices. Matrix sandwich problems are an important special case of matrix completion problems, the latter being generally defined over the real numbers rather than simply {0,1}.

Original language	English
Pages (from-to)	239-251
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	277
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(97)10075-1
State	Published - 15 Jun 1998
Externally published	Yes

Keywords

Block decomposition of matrices
Ferrers diagrams
Forbidden submatrix problems
Matrix completion problems
Matrix sandwich problems

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(97)10075-1

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AB - The Π Matrix Sandwich Problem (Π-MSP) is introduced here as follows: Given a {0, 1, *} valued matrix A, where * is interpreted as "do not care", does there exist a fill-in of the asterisks * with 0s and 1s such that the completed {0, 1} valued matrix M satisfies property Π? We study the computational complexity of this problem for several matrix properties including the Ferrers property, block decompositions and certain forbidden submatrices. Matrix sandwich problems are an important special case of matrix completion problems, the latter being generally defined over the real numbers rather than simply {0,1}.

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ER -

Matrix sandwich problems

Abstract

Keywords

ASJC Scopus subject areas

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