A tight bound on approximating arbitrary metrics by tree metrics
نویسندگان
چکیده
منابع مشابه
On approximating planar metrics by tree metrics
We combine the results of Bartal [Proc. 37th FOCS, 1996, pp. 184–193] on probabilistic approximation of metric spaces by tree metrics, with those of Klein, Plotkin and Rao [Proc. 25th STOC, 1993, pp. 682–690] on decompositions of graphs without small Ks,s minors (such as planar graphs) to show that metrics induced by such graphs (with unit lengths on the edges) can be probabilistically approxim...
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We study the problem of how well a tree metric is able to preserve the sum of pairwisedistances of an arbitrary metric. This problem is closely related to low-stretch metricembeddings and is interesting by its own flavor from the line of research proposed in theliterature.As the structure of a tree imposes great constraints on the pairwise distances, any embed-ding of a ...
متن کاملApproximating snowflake metrics by trees
Article history: Received 25 January 2015 Received in revised form 4 November 2015 Accepted 7 October 2016 Available online xxxx Communicated by Charles K. Chui MSC: 68W05 68W25 05C05 54E35
متن کاملComments on "On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension"
Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824–831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in Z. In this note we compare this approximation to two previously ...
متن کاملA note on approximating snowflake metrics by trees
prove that the tree construction of Fakcharoenphol, Rao, and Talwar [2] can be used to approximate snowflake metrics by trees with expected distortion bounded independently of the size of the metric space. The constant of distortion we derive depends linearly on the dimension of the metric space. We also present an algorithm for building a single tree whose cost is linear in the problem size. A...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2004
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2004.04.011