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