### Abstract

A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. A c-vertex-ranking is optimal if the number of labels used is as small as possible. We present sequential and parallel algorithms to find an optimal c-vertex-ranking of a partial k-tree, that is, a graph of treewidth bounded by a fixed integer k. The sequential algorithm takes polynomial-time for any positive integer c. The parallel algorithm takes O(log n) parallel time using a polynomial number of processors on the common CRCW PRAM, where n is the number of vertices in G.

Original language | English |
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Pages (from-to) | 407-427 |

Number of pages | 21 |

Journal | Theoretical Computer Science |

Volume | 240 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2000 Jun 17 |

### Keywords

- Algorithm
- Partial k-tree
- Separator tree
- Treewidth
- Vertex-ranking

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*240*(2), 407-427. https://doi.org/10.1016/S0304-3975(99)00240-6