### Abstract

In this paper we newly define a generalized edge-ranking of a graph G as follows: for a positive integer c, a c-edge-ranking of G is a labeling (ranking) of the edges of G with integers such that, for any label i, deletion of all edges with labels > i leaves connected components, each having at most c edges with label i. The problem of finding an optimal c-edge-ranking of G, that is, a c-edge-ranking using the minimum number of ranks, has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding a c-edge-separator tree of G having the minimum height. We present an algorithm to find an optimal c-edge-ranking of a given tree T for any positive integer c in time 0(n^{2} log Δ), where n is the number of vertices in T and Δ is the maximum vertex-degree of T. Our algorithm is faster than the best algorithm known for the case c = 1.

Original language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 22nd International Workshop, WG 1996, Proceedings |

Pages | 390-404 |

Number of pages | 15 |

DOIs | |

Publication status | Published - 1997 Dec 1 |

Event | 22nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1996 - Cadenabbia, Italy Duration: 1996 Jun 12 → 1996 Jun 14 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1197 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1996 |
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Country | Italy |

City | Cadenabbia |

Period | 96/6/12 → 96/6/14 |

### Keywords

- Algorithm
- Edge-ranking
- Separator tree
- Tree

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Graph-Theoretic Concepts in Computer Science - 22nd International Workshop, WG 1996, Proceedings*(pp. 390-404). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1197 LNCS). https://doi.org/10.1007/3-540-62559-3_31