### Abstract

Let G be a simple graph in which each vertex v has a positive integer weight b(v) and each edge (v,w) has a nonnegative integer weight b(v,w). A bandwidth consecutive multicoloring of G assigns each vertex v a specified number b(v) of consecutive positive integers so that, for each edge (v,w), all integers assigned to vertex v differ from all integers assigned to vertex w by more than b(v,w). The maximum integer assigned to a vertex is called the span of the coloring. In the paper, we first investigate fundamental properties of such a coloring. We then obtain a pseudo polynomial-time exact algorithm and a fully polynomial-time approximation scheme for the problem of finding such a coloring of a given series-parallel graph with the minimum span. We finally extend the results to the case where a given graph G is a partial k-tree, that is, G has a bounded tree-width.

Original language | English |
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Title of host publication | Frontiers in Algorithmics and Algorithmic Aspects in Information and Management - Joint International Conference, FAW-AAIM 2012, Proceedings |

Pages | 117-128 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2012 May 23 |

Event | 6th International Frontiers of Algorithmics Workshop, FAW 2012 and 8th International Conference on Algorithmic Aspects of Information and Management, AAIM 2012 - Beijing, China Duration: 2012 May 14 → 2012 May 16 |

### 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 | 7285 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Frontiers of Algorithmics Workshop, FAW 2012 and 8th International Conference on Algorithmic Aspects of Information and Management, AAIM 2012 |
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Country | China |

City | Beijing |

Period | 12/5/14 → 12/5/16 |

### Keywords

- Acyclic orientation
- Algorithm
- Approximation
- Bandwidth coloring
- Channel assignment
- FPTAS
- Multicoloring
- Partial k-tree
- Series-parallel graph

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Frontiers in Algorithmics and Algorithmic Aspects in Information and Management - Joint International Conference, FAW-AAIM 2012, Proceedings*(pp. 117-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7285 LNCS). https://doi.org/10.1007/978-3-642-29700-7_11