### Abstract

In this paper we introduce and study a new problem named min-max edge q-coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge q-coloring is NP-hard, for any q ≥ 2. 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. 3. Exact formulas of the optimal solution for cliques. 4. An approximation algorithm for planar graphs.

Original language | English |
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Title of host publication | Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 226-237 |

Number of pages | 12 |

Volume | 8986 |

ISBN (Print) | 9783319193144 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

Event | 25th International Workshop on Combinatorial Algorithms, IWOCA 2014 - Duluth, United States Duration: Oct 15 2014 → Oct 17 2014 |

### 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 | 8986 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 25th International Workshop on Combinatorial Algorithms, IWOCA 2014 |
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Country | United States |

City | Duluth |

Period | 10/15/14 → 10/17/14 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers*(Vol. 8986, pp. 226-237). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8986). Springer Verlag. https://doi.org/10.1007/978-3-319-19315-1_20

**The min-max Edge q-Coloring Problem.** / Larjomaa, Tommi; Popa, Alexandru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers.*vol. 8986, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8986, Springer Verlag, pp. 226-237, 25th International Workshop on Combinatorial Algorithms, IWOCA 2014, Duluth, United States, 10/15/14. https://doi.org/10.1007/978-3-319-19315-1_20

}

TY - GEN

T1 - The min-max Edge q-Coloring Problem

AU - Larjomaa, Tommi

AU - Popa, Alexandru

PY - 2015

Y1 - 2015

N2 - In this paper we introduce and study a new problem named min-max edge q-coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge q-coloring is NP-hard, for any q ≥ 2. 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. 3. Exact formulas of the optimal solution for cliques. 4. An approximation algorithm for planar graphs.

AB - In this paper we introduce and study a new problem named min-max edge q-coloring which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer q. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most q different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge q-coloring is NP-hard, for any q ≥ 2. 2. A polynomial time exact algorithm for min-max edge q-coloring on trees. 3. Exact formulas of the optimal solution for cliques. 4. An approximation algorithm for planar graphs.

UR - http://www.scopus.com/inward/record.url?scp=84937485497&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937485497&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-19315-1_20

DO - 10.1007/978-3-319-19315-1_20

M3 - Conference contribution

SN - 9783319193144

VL - 8986

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 226

EP - 237

BT - Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers

PB - Springer Verlag

ER -