# Computing the Gromov-Hausdorff distance for metric trees

Published

Journal Article

© Springer-Verlag Berlin Heidelberg 2015. The Gromov-Hausdorff distance is a natural way to measure distance between two metric spaces. We give the first proof of hardness and first non-trivial approximation algorithm for computing the Gromov-Hausdorff distance for geodesic metrics in trees. Specifically, we prove it is NP-hard to approximate the Gromov-Hausdorff distance better than a factor of 3. We complement this result by providing a polynomial time O(min{n, √rn})-approximation algorithm where r is the ratio of the longest edge length in both trees to the shortest edge length. For metric trees with unit length edges, this yields an O(√ n)-approximation algorithm.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Fox, K; Nath, A; Sidiropoulos, A; Wang, Y

### Published Date

- January 1, 2015

### Published In

### Volume / Issue

- 9472 /

### Start / End Page

- 529 - 540

### Electronic International Standard Serial Number (EISSN)

- 1611-3349

### International Standard Serial Number (ISSN)

- 0302-9743

### Digital Object Identifier (DOI)

- 10.1007/978-3-662-48971-0_45

### Citation Source

- Scopus