### Abstract

Let P be a property of undirected graphs. We consider the following problem: given a graph G that has property P, find a minimal spanning subgraph of G with property P. We describe two related algorithms for this problem and prove their correctness under some rather weak assumptions about P. We devise a general technique for analyzing the worst-case behavior of these algorithms. By applying the technique to 2-edge-connectivity and biconnectivity, we obtain an ω(m + n log n) lower bound on the worst-case running time of the algorithms for these two properties, thus settling open questions posed earlier with regard to these properties. We then describe refinements of the basic algorithms that yield the first linear-time algorithms for finding a minimal 2-edge-connected spanning subgraph and a minimal biconnected spanning subgraph of a graph.

Original language | English (US) |
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Title of host publication | Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |

Publisher | Association for Computing Machinery |

Pages | 146-156 |

Number of pages | 11 |

ISBN (Electronic) | 089791466X |

State | Published - Sep 1 1992 |

Event | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States Duration: Jan 27 1992 → Jan 29 1992 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | Part F129721 |

### Other

Other | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |
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Country | United States |

City | Orlando |

Period | 1/27/92 → 1/29/92 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992*(pp. 146-156). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. Part F129721). Association for Computing Machinery.