Avoiding Forbidden Submatrices by Row Deletions
نویسندگان
چکیده
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.
منابع مشابه
The Computational Complexity of Avoiding Forbidden Submatrices by Row Deletions
We initiate a systematic study of the Row Deletion(B) problem on matrices: Given an input matrix A and a fixed “forbidden submatrix” B, the task is to remove a minimum number of rows from A such that no row or column permutation of B occurs as a submatrix in the resulting matrix. An application of this problem can be found, for instance, in the construction of perfect phylogenies. Establishing ...
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