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### Classical Complexity and Fixed-Parameter Tractability of Simultaneous Consecutive Ones Submatrix & Editing Problems [chapter]

M. R. Rani, Mohith Jagalmohanan, R. Subashini
2018 Lecture Notes in Computer Science
A binary matrix M has the consecutive ones property (C1P ) for rows (resp. columns) if there is a permutation of its columns (resp. rows) that arranges the ones consecutively in all the rows (resp. columns  ...  If M has the C1P for rows and the C1P for columns, then M is said to have the simultaneous consecutive ones property (SC1P ).  ...  We also observe that the fixed-parameter tractability of d-SC1S-R problem on (2, * )matrices shows that proper interval vertex deletion problem is FPT on triangle free graphs with a run-time of O * (4  ...

### Matrix sandwich problems

Martin Charles Golumbic
1998 Linear Algebra and its Applications
We study the computational complexity of this problem for several matrix properties including the Ferrers property, block decompositions and certain forbidden submatrices.  ...  ls such that the completed {0, 1} valued matrix M satisfies property/7?  ...  Acknowledgements The author would like to thank Vadim Levit and Moshe Lewenstein for our many useful discussions on sandwich problems.  ...

### Simultaneous Consecutive Ones Submatrix and Editing Problems : Classical Complexity & Fixed-Parameter Tractable Results [article]

M R Rani, R Subashini, Mohith Jagalmohanan
2018 arXiv   pre-print
A binary matrix M has the consecutive ones property (C1P) for rows (resp. columns) if there is a permutation of its columns (resp. rows) that arranges the ones consecutively in all the rows (resp. columns  ...  If M has the C1P for rows and columns, then M is said to have the simultaneous consecutive ones property (SC1P).  ...  A binary matrix has the consecutive ones property (C1P) for rows (resp. columns)  , if there is a permutation of its columns (resp. rows) that arranges the ones consecutively in all the rows (resp.  ...

### Incidence matrices and interval graphs

Delbert Fulkerson, Oliver Gross
1965 Pacific Journal of Mathematics
The problem of determining when a graph is an interval graph is a special case of the following problem concerning (0, l)-matrices: When can the rows of such a matrix be permuted so as to make the l's  ...  one exists.  ...  The Pacific Journal of Mathematics is published quarterly, in March, June, September, and December. Effective with Volume 13 the price per volume (4 numbers) is \$18.00; single issues, \$5.00.  ...

### On Finding Lekkerkerker-Boland Subgraphs [article]

Nathan Lindzey, Ross McConnell
2013 arXiv   pre-print
Tucker characterized the minimal forbidden submatrices of matrices that do not have the consecutive-ones property.  ...  We give a linear-time algorithm to find one in any matrix that does not have the consecutive-ones property.  ...  The paper dealt with arbitrary consecutive-ones matrices where such rows need not occur. Lemma 12.  ...

### Very Fast Instances for Concept Generation [chapter]

Anne Berry, Ross M. McConnell, Alain Sigayret, Jeremy P. Spinrad
2006 Lecture Notes in Computer Science
Computing the maximal bicliques of a bipartite graph is equivalent to generating the concepts of the binary relation defined by the matrix of this graph.  ...  We study this problem for special classes of input relations for which concepts can be generated much more efficiently than in the general case; in some special cases, we can even say that the number of  ...  Consecutive-Ones Matrices The starting point for this research is the consecutive ones property.  ...

### On the additive structure of the inverses of banded matrices

Francesco Romani
1986 Linear Algebra and its Applications
The additive structure of the inverses of banded matrices is investigated.  ...  In the nonsymmetric case, a more complicated structure is obtained. Applications are mentioned for the resolution of coustant coefficient banded linear systems in VLSI models.  ...  The submatrix Q is obtained from B by deleting k consecutive rows and columns and is nonsingular because B is proper.  ...

### Linear-Time Algorithms for Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs [article]

Nathan Lindzey, Ross M. McConnell
2013 arXiv   pre-print
Tucker characterized the minimal forbidden submatrices of binary matrices that do not have the consecutive-ones property.  ...  We give a linear-time algorithm to find one in any binary matrix that does not have the consecutive-ones property.  ...  These are the matrices that do not have the consecutive-ones property, but where deletion of any row or column results in a matrix that has the consecutive-ones property.  ...

### A Heuristic Approach to the Consecutive Ones Submatrix Problem

Given a (0, 1) −matrix, the Consecutive Ones Submatrix (C1S) problem which aims to find the permutation of columns that maximizes the number of columns having together only one block of consecutive ones  ...  A heuristic approach will be suggested to solve the problem. Also, the Consecutive Blocks Minimization (CBM) problem which is related to the consecutive ones submatrix will be considered.  ...  Acknowledgments: The authors would like to thank Schöbel, one of the authors of that provided us with real-world data. Also, to Omar Kirikcki for supplying us with the random nonsymmetric matrices.  ...

### Properties of (0, 1)-matrices with no triangles

R.P Anstee
1980 Journal of combinatorial theory. Series A
We study (0, I)-matrices which contain no triangles (submatrices of order 3 with row and column sums 2) previously studied by Ryser.  ...  For matrices with no triangles, columns sums >2, we find that the number of linearly independent row intersections is equal to the number of distinct columns.  ...  ACKNOWLEDGMENTS The author wishes to thank Dr. H. J. Ryser for the careful scrutiny he gave this paper.  ...

### On Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs [chapter]

Nathan Lindzey, Ross M. McConnell
2013 Lecture Notes in Computer Science
Tucker characterized the minimal forbidden submatrices of matrices that do not have the consecutive-ones property.  ...  We give a linear-time algorithm to find one in any matrix that does not have the consecutive-ones property. ⋆  ...  By induction on i, M does not have the consecutive-ones property at the end of iteration i.  ...

### Graph Isomorphism and Identification Matrices: Sequential Algorithms

Lin Chen
1999 Journal of computer and system sciences (Print)
We show that, given two graphs represented by two identification matrices with respect to a certain relation, isomorphism can be decided efficiently if at least one matrix satisfies the consecutive 1's  ...  Graphs which have identification matrices satisfying the consecutive 1's property include, among others, proper interval graphs and doubly convex bipartite graphs.  ...  Input: Two matrices M 1 and M 2 with the consecutive 1's property for rows.  ...

### d-COS-R is FPT via Interval Deletion [article]

N.S. Narayanaswamy, R. Subashini
2013 arXiv   pre-print
A binary matrix M has the Consecutive Ones Property (COP) if there exists a permutation of columns that arranges the ones consecutively in all the rows.  ...  We consider the parameterized complexity of this problem with respect to the number d of rows to be deleted as the parameter.  ...  The algorithm returns a set D of at most d rows (if one exists) such that G[V 1 \ D, V 2 ] is convex bipartite where D is the subset of vertices of V 1 corresponding to D.  ...

### A selected tour of the theory of identification matrices

Lin Chen
2000 Theoretical Computer Science
Additionally, we provide an improved proof that augmented adjacency matrices satisfying the circular 1's property are identiÿcation matrices.  ...  Based on the theory of identiÿcation matrices, we describe an improved method for testing isomorphism between circular arc graphs.  ...  Acknowledgements During the course of my work on the theory of identiÿcation matrices and the graph isomorphism problem, I have met and talked with many scientists. In particular,  ...

### Approximation and fixed-parameter algorithms for consecutive ones submatrix problems

Michael Dom, Jiong Guo, Rolf Niedermeier
2010 Journal of computer and system sciences (Print)
We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P).  ...  This characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the NP-hard problem to delete a minimum number of rows or columns from  ...  Thus, a binary matrix M has the Circ1P if by permuting its columns a matrix M can be obtained with the following property: If M is wrapped around a vertical cylinder, then the 1s appear consecutively in  ...
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