### Abstract

Original language | Undefined |
---|---|

Title of host publication | Computer Science – Theory and Applications: Proceedings 6th International Computer Science Symposium in Russia, CSR 2011 |

Editors | A. Kulikov, N. Vereshchagin |

Place of Publication | Heidelberg |

Publisher | Springer |

Pages | 443-455 |

Number of pages | 13 |

ISBN (Print) | 978-3-642-20711-2 |

DOIs | |

Publication status | Published - Jun 2011 |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Publisher | Springer Verlag |

Volume | 6651 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Keywords

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

### Cite this

*Computer Science – Theory and Applications: Proceedings 6th International Computer Science Symposium in Russia, CSR 2011*(pp. 443-455). (Lecture Notes in Computer Science; Vol. 6651). Heidelberg: Springer. https://doi.org/10.1007/978-3-642-20712-9_35

}

*Computer Science – Theory and Applications: Proceedings 6th International Computer Science Symposium in Russia, CSR 2011.*Lecture Notes in Computer Science, vol. 6651, Springer, Heidelberg, pp. 443-455. https://doi.org/10.1007/978-3-642-20712-9_35

**Recognizing sparse perfect elimination bipartite graphs.** / Bomhoff, M.J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Recognizing sparse perfect elimination bipartite graphs

AU - Bomhoff, M.J.

N1 - 10.1007/978-3-642-20712-9_35

PY - 2011/6

Y1 - 2011/6

N2 - 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 $O(n m)$

AB - 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 $O(n m)$

KW - METIS-284944

KW - Perfect elimination – algorithms – bipartite graphs – sparse graphs

KW - EWI-21125

KW - IR-79141

U2 - 10.1007/978-3-642-20712-9_35

DO - 10.1007/978-3-642-20712-9_35

M3 - Conference contribution

SN - 978-3-642-20711-2

T3 - Lecture Notes in Computer Science

SP - 443

EP - 455

BT - Computer Science – Theory and Applications: Proceedings 6th International Computer Science Symposium in Russia, CSR 2011

A2 - Kulikov, A.

A2 - Vereshchagin, N.

PB - Springer

CY - Heidelberg

ER -