## Abstract

We introduce and study the notion of the average distortion of a nonexpanding embedding of one metric space into another. Less sensitive than the multiplicative metric distortion, the average distortion captures well the global picture, and, overall, is a quite interesting new measure of metric proximity, related to the concentration of measure phenomenon. We establish close mutual relations between the MinCut - MaxFlow gap in a uniform-demand multicommodity flow, and the average distortion of embedding the suitable (dual) metric into l_{1}, These relations are exploited to show that the shortest-path metrics of special (e.g., planar, bounded treewidth, etc.) graphs embed into l_{1} with constant average distortion. The main result of the paper claims that this remains true even if l_{1} is replaced with the line. This result is further sharpened for graphs of a bounded treewidth.

Original language | English |
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Pages (from-to) | 456-462 |

Number of pages | 7 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 2003 |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: 9 Jun 2003 → 11 Jun 2003 |

## Keywords

- Average metric distortion
- Finite metric spaces
- Planar metrics

## ASJC Scopus subject areas

- Software