A note on perfect partial elimination

Matthijs J. Bomhoff, Walter Kern, Georg J. Still

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In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard.
Original languageEnglish
Pages (from-to)1558-1563
Number of pages6
JournalDiscrete mathematics
Issue number14
Publication statusPublished - 2013


  • Perfect elimination
  • Bipartite graph
  • Gaussian elimination
  • Complexity


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