Approximability and Parameterized Complexity of Consecutive Ones Submatrix Problems
We develop a refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the problem to find a maximum-size submatrix of a 0/1-matrix such that the submatrix has the C1P. Moreover, we achieve a problem kernelization based on simple data reduction rules and provide several search tree algorithms. Finally, we derive inapproximability results.
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