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Algorithms"],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"<jats:p>\n            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\u00a03 for geodesic metrics on a pair of trees. We complement this result by providing a polynomial time\n            <jats:italic>O<\/jats:italic>\n            (min\n            <jats:italic>n<\/jats:italic>\n            , \u221a\n            <jats:italic>rn<\/jats:italic>\n            )-approximation algorithm for computing the GH distance between a pair of metric trees, where\u00a0\n            <jats:italic>r<\/jats:italic>\n            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\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            )-approximation algorithm\n            <jats:sup>1<\/jats:sup>\n            .\n          <\/jats:p>","DOI":"10.1145\/3185466","type":"journal-article","created":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T17:21:50Z","timestamp":1524072110000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["Computing the Gromov-Hausdorff Distance for Metric Trees"],"prefix":"10.1145","volume":"14","author":[{"given":"Pankaj K.","family":"Agarwal","sequence":"first","affiliation":[{"name":"Duke University, Durham NC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyle","family":"Fox","sequence":"additional","affiliation":[{"name":"The University of Texas at Dallas, Richardson, TX USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abhinandan","family":"Nath","sequence":"additional","affiliation":[{"name":"Duke University, Durham NC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anastasios","family":"Sidiropoulos","sequence":"additional","affiliation":[{"name":"University of Illinois at Chicago, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusu","family":"Wang","sequence":"additional","affiliation":[{"name":"Ohio State University, Columbus, OH"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,4,16]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48971-0_45"},{"key":"e_1_2_1_2_1","volume-title":"Ullman","author":"Aho Alfred V.","year":"1974"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2582112.2582169"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/1237762.1237774"},{"key":"e_1_2_1_5_1","volume-title":"A Course in Metric Geometry","author":"Burago Dmitri"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/1756006.1859898"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-016-9763-9"},{"key":"e_1_2_1_8_1","unstructured":"Tamal K. Dey Dayu Shi and Yusu Wang. 2015. Comparing graphs via persistence distortion. CoRR abs\/1503.07414. http:\/\/arxiv.org\/abs\/1503.07414  Tamal K. Dey Dayu Shi and Yusu Wang. 2015. Comparing graphs via persistence distortion. CoRR abs\/1503.07414. http:\/\/arxiv.org\/abs\/1503.07414"},{"key":"e_1_2_1_9_1","volume-title":"Proc. Int. Symp. Comput. Geom. 491--506","author":"Dey Tamal K.","year":"2015"},{"key":"e_1_2_1_10_1","volume-title":"Johnson","author":"Garey M. R.","year":"1979"},{"key":"e_1_2_1_11_1","volume-title":"Metric Structures for Riemannian and Non-Riemannian Spaces","author":"Gromov Mikhail"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/11538462_10"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/0202019"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/1957995.1958014"},{"key":"e_1_2_1_15_1","volume-title":"Proc. Symp. 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