Abstract
We initiate a systematic study of the Row Deletion( B ) problem on matrices: For a fixed “forbidden submatrix” B, the question is, given an input matrix A (both A and B have entries chosen from a finite-size alphabet), to remove a minimum number of rows such that A has no submatrix which is equivalent to a row or column permutation of B. An application of this question can be found, e.g., in the construction of perfect phylogenies. Establishing a strong connection to variants of the NP-complete Hitting Set problem, we show that for most matrices B Row Deletion( B ) is NP-complete. On the positive side, the relation with Hitting Set problems yields constant-factor approximation algorithms and fixed-parameter tractability results.
Supported by the Deutsche Forschungsgemeinschaft (DFG), project PEAL (parameterized complexity and exact algorithms), NI 369/1; project OPAL (optimal solutions for hard problems in computational biology), NI 369/2; junior research group “PIAF” (fixed-parameter algorithms), NI 369/4.
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Wernicke, S., Alber, J., Gramm, J., Guo, J., Niedermeier, R. (2004). Avoiding Forbidden Submatrices by Row Deletions. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2004: Theory and Practice of Computer Science. SOFSEM 2004. Lecture Notes in Computer Science, vol 2932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24618-3_30
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DOI: https://doi.org/10.1007/978-3-540-24618-3_30
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