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Simultaneous Consecutive Ones Submatrix and Editing Problems : Classical Complexity \& Fixed-Parameter Tractable Results
A binary matrix has the consecutive ones property () 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 has the
for rows and columns, then is said to have the simultaneous consecutive
ones property (). In this article, we consider the classical complexity
and fixed-parameter tractability of Simultaneous Consecutive Ones
Submatrix () and Simultaneous Consecutive Ones Editing ()
[Oswald et al., Theoretical Comp. Sci. 410(21-23):1986-1992,
\hyperref[references]{2009}] problems. We show that the decision versions of
and problems are NP-complete. We consider the parameterized
versions of and problems with , being the solution size, as
the parameter. Given a binary matrix and a positive integer ,
--, --, and -- problems decide whether
there exists a set of rows, columns, and rows as well as columns, respectively,
of size at most , whose deletion results in a matrix with the . The
--, --, and -- problems decide whether
there exists a set of -entries, -entries, and -entries as well as
-entries, respectively, of size at most , whose flipping results in a
matrix with the \vspace{0.095 in} .Comment: A preliminary version of this paper appeared in the proceedings of
the 12th International Frontiers of Algorithmics Workshop (FAW 2018