## Abstract

We initiate the study of the minimum distortion problem: given as input two n-point metric spaces, find a bijection between them with minimum distortion. This is an abstraction of certain geometric problems in shape and image matching, and is also a natural variation and extension of the fundamental problems of graph isomorphism and bandwidth. Our focus is on algorithms that find an optimal (or near-optimal) bijection when the distortion is fairly small. We present a polynomial time algorithm that finds an optimal bijection between two line metrics, provided the distortion is less than 3 + 2√2. We also give a parameterized polynomial time algorithm that finds an optimal bijection between an arbitrary unweighted graph metric and a bounded-degree tree metric.

Original language | American English |
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Pages (from-to) | 272-280 |

Number of pages | 9 |

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

DOIs | |

State | Published - 2004 |

Externally published | Yes |

Event | Proceedings of the 36th Annual ACM Symposium on Theory of Computing - Chicago, IL, United States Duration: 13 Jun 2004 → 15 Jun 2004 |

## Keywords

- Dynamic programming
- Low distortion embeddings
- Metric spaces
- Shape matching