Avoiding Forbidden Submatrices by Row Deletions
- Cite this paper as:
- 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
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 BRow 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.
Unable to display preview. Download preview PDF.