Avoiding Forbidden Submatrices by Row Deletions

  • Sebastian Wernicke
  • Jochen Alber
  • Jens Gramm
  • Jiong Guo
  • Rolf Niedermeier
Conference paper

DOI: 10.1007/978-3-540-24618-3_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2932)
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

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 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sebastian Wernicke
    • 1
  • Jochen Alber
    • 1
  • Jens Gramm
    • 1
  • Jiong Guo
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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