## Abstract

We show that the shortest-path metric of any k-outerplanar graph, for any fixed k, can be approximated by a probability distribution over tree metrics with constant distortion, and hence also embedded into ℓ_{1} with constant distortion. These graphs play a central role in polynomial time approximation schemes for many NP-hard optimization problems on general planar graphs, and include the family of weighted k × n planar grids. This result implies a constant upper bound on the ratio between the sparsest cut and the maximum concurrent flow in multicommodity networks for k-outerplanar graphs, thus extending a classical theorem of Okamura and Seymour [26] for outerplanar graphs, and of Gupta et al. [17] for treewidth-2 graphs. In addition, we obtain improved approximation ratios for k-outerplanar graphs on various problems for which approximation algorithms are based on probabilistic tree embeddings. We also conjecture that our random tree embeddings for k-outerplanar graphs can serve as a building block for more powerful ℓ_{1} embeddings in future.

Original language | English |
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Pages | 527-536 |

Number of pages | 10 |

State | Published - 2003 |

Event | Configuralble Computing: Technology and Applications - Boston, MA, United States Duration: 2 Nov 1998 → 3 Nov 1998 |

### Conference

Conference | Configuralble Computing: Technology and Applications |
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Country/Territory | United States |

City | Boston, MA |

Period | 2/11/98 → 3/11/98 |

## ASJC Scopus subject areas

- Software
- General Mathematics

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