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

2018
*
Lecture Notes in Computer Science
*

A binary matrix M has

doi:10.1007/978-3-319-78455-7_12
fatcat:c2sptpgoqrg4xgsncvuzvjcyca
*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

1998
*
Linear Algebra and its Applications
*

We study

doi:10.1016/s0024-3795(97)10075-1
fatcat:7xmw4p3vozg6thnm47wfpltzd4
*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]

2018
*
arXiv
*
pre-print

A binary matrix M has

arXiv:1707.00106v5
fatcat:7pxx5euhv5debcwrtfhee4umri
*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) [5] , 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

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. ...

##
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On Finding Lekkerkerker-Boland Subgraphs
[article]

2013
*
arXiv
*
pre-print

Tucker characterized

arXiv:1303.1840v1
fatcat:25wggz7pzvabvkcgo76bgdla6i
*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]

2006
*
Lecture Notes in Computer Science
*

Computing

doi:10.1007/11671404_8
fatcat:aghlksxrpbezjkqhdczk5prcge
*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

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]

2013
*
arXiv
*
pre-print

Tucker characterized

arXiv:1401.0224v1
fatcat:pc4ahp4lwrc5hb7jiq7m3w73wy
*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

2022
*
Baghdad Science Journal
*

Given a (0, 1) −matrix,

doi:10.21123/bsj.2022.6373
fatcat:zwbowes2grcojg3gqgqpmrh67u
*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

1980
*
Journal of combinatorial theory. Series A
*

We study (0, I)-

doi:10.1016/0097-3165(80)90008-4
fatcat:3tp57nbat5huhdvwdtsb376fki
*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]

2013
*
Lecture Notes in Computer Science
*

Tucker characterized

doi:10.1007/978-3-642-45043-3_30
fatcat:6awdt37pcffhzcigpwljm4sjku
*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

1999
*
Journal of computer and system sciences (Print)
*

We show that, given two graphs represented

doi:10.1006/jcss.1999.1642
fatcat:py2pmr5i55aq3l3uuiw7mvqxce
*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]

2013
*
arXiv
*
pre-print

A binary matrix M has

arXiv:1303.1643v1
fatcat:bar5qkmmrzburaeliuvzqxlrqm
*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

2000
*
Theoretical Computer Science
*

Additionally, we provide an improved proof that augmented adjacency

doi:10.1016/s0304-3975(99)00236-4
fatcat:htxrnsidrvhx5p3ucqkne3lj5u
*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

2010
*
Journal of computer and system sciences (Print)
*

We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-

doi:10.1016/j.jcss.2009.07.001
fatcat:peky25yumnho3e6m4znernjj4i
*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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