### Abstract

Colbourn, Day, and Nel developed the first algorithm requiring at most O(n^{3}) arithmetic operations for ranking and unranking spanning trees of a graph (n is the number of vertices of the graph). We present two algorithms for the more general problem of ranking and unranking rooted spanning arborescences of a directed graph. The first is conceptually very simple and requires O(n^{3}) arithmetic operations. The second approach shows that the number of arithmetic operations can be reduced to the same as that of the best known algorithms for matrix multiplication.

Original language | English (US) |
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Pages (from-to) | 268-281 |

Number of pages | 14 |

Journal | Journal of Algorithms |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1996 |

Externally published | Yes |

### ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics

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## Cite this

Colbourn, C. J., Myrvold, W. J., & Neufeld, E. (1996). Two Algorithms for Unranking Arborescences.

*Journal of Algorithms*,*20*(2), 268-281. https://doi.org/10.1006/jagm.1996.0014