## Abstract

We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (2007) and Bǎdoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K_{2,3}, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.

Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings |

Pages | 95-109 |

Number of pages | 15 |

DOIs | |

State | Published - 2010 |

Event | 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain Duration: 1 Sep 2010 → 3 Sep 2010 |

### 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 | 6302 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 |
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Country/Territory | Spain |

City | Barcelona |

Period | 1/09/10 → 3/09/10 |

### Bibliographical note

Funding Information:This research was partly supported by the ANR grant BLANC GGAA.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science