Math @ Duke
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Publications [#337581] of Pankaj K. Agarwal
Papers Published
- Agarwal, PK; Kyle, FOX; Nath, A; Sidiropoulos, A; Wang, Y, Computing the gromov-hausdorff distance for metric trees,
Acm Transactions on Algorithms, vol. 14 no. 2
(June, 2018),
pp. 1-20, Association for Computing Machinery (ACM) [doi]
(last updated on 2023/06/02)
Abstract: The Gromov-Hausdorff (GH) distance is a natural way to measure distance between two metric spaces. We prove that it is NP-hard to approximate the GH distance better than a factor of 3 for geodesic metrics on a pair of trees. We complement this result by providing a polynomial time O(min{n, rn})-approximation algorithm for computing the GH distance between a pair of metric trees, 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.1
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