Recognizing sparse perfect elimination bipartite graphs

M.J. Bomhoff

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When applying Gaussian elimination to a sparse matrix, it is desirable to avoid turning zeros into nonzeros to preserve sparsity. Perfect elimination bipartite graphs are closely related to square matrices that Gaussian elimination can be applied to without turning any zero into a nonzero. Existing literature on the recognition of these graphs mainly focuses on time complexity. For $n \times n$ matrices with $m$ nonzero elements, the best known algorithm runs in time $O(n^3/\log n)$. However, the space complexity also deserves attention: it may not be worthwhile to look for suitable pivots for a sparse matrix if this requires $\Omega(n^2)$ space. We present two new recognition algorithms for sparse instances: one with a $O(n m)$ time complexity in $\Theta(n^2)$ space and one with a $O(m^2)$ time complexity in $\Theta(m)$ space. Furthermore, if we allow only pivots on the diagonal, our second algorithm is easily adapted to run in time $O(n m)$
Original languageUndefined
Title of host publicationComputer Science – Theory and Applications: Proceedings 6th International Computer Science Symposium in Russia, CSR 2011
EditorsA. Kulikov, N. Vereshchagin
Place of PublicationHeidelberg
Number of pages13
ISBN (Print)978-3-642-20711-2
Publication statusPublished - Jun 2011
EventComputer Science – Theory and Applications - St. Petersburg, Russia
Duration: 14 Jun 201118 Jun 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceComputer Science – Theory and Applications
Other14-18 June 2011


  • METIS-284944
  • Perfect elimination – algorithms – bipartite graphs – sparse graphs
  • EWI-21125
  • IR-79141

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