Computing the Gromov-Hausdorff distance for metric trees


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