FPT Algorithms for Consecutive Ones Submatrix Problems

Interval Deletion Is Fixed-Parameter Tractable

“…As having been explored in [31], we would also like to ask which other problems can be formulated as or reduced to INTERVAL DELETION and then solved with our algorithm. Both practical and theoretical consequences are worth further investigation.…”

“…For interval graphs, the fixed-parameter tractability of the completion problem was raised as an open question by Kaplan et al [20] in 1994, to which a positive answer with a k 2k · n O(1) -time algorithm was given by Villanger et al [35] in 2007. In this paper, we answer the complementary question on vertex deletion: Narayanaswamy and Subashini [31] recently used Theorem 1.1 as a subroutine to solve the maximum CON-SECUTIVE ONES SUB -MATRIX problem and the minimum CONVEX BIPARTITE DELETION problem.…”

“…Narayanaswamy and Subashini [31] recently used Theorem 1.1 as a subroutine to solve the maximum CON-SECUTIVE ONES SUB -MATRIX problem and the minimum CONVEX BIPARTITE DELETION problem.…”

Linear Recognition of Almost Interval Graphs

“…In light of the importance of interval graphs, it is not surprising that some natural combinatorial problems can be formulated as, or computationally reduced to the interval deletion problems. For instance, Narayanaswamy and Subashini [76] recently solved the maximum consecutive ones sub-matrix problem and the minimum convex bipartite deletion problem by a reduction to minimum interval vertex deletion. Oum et al [79] showed that an induced interval subgraph can be used to find a special branch decomposition, which can be in turn used to devise FPT algorithms for a large number of problems, namely, locally checkable vertex subset and vertex partitioning problems.…”

“…But as finding Tucker sub-matrices is as least as hard as finding non-interval subgraphs, there is little hope to find a minimum one in the same time. Can our techniques be applied to solve modification problems related to C1P ( [29,76])?…”