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On approximating arbitrary metrics by tree metrics

On approximating arbitrary metrics by tree metrics,Y. Bartal

On approximating arbitrary metrics by tree metrics   (Citations: 117)
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    • ...HSTs: Study of HSTs initially focused on approximating metrics using trees [2], [3], [7], while more recent work examines the way HSTs can enable efficient resource management and matching in sensor networks [9]...
    • ...The original motivation for the HST was given by Bartal [2], [3], who proposed the idea of approximating metrics using a distribution over trees...

    Arik Motskinet al. Network warehouses: Efficient information distribution to mobile users

    • ...Using the fact that every graph metric can be probabilistically embedded into a tree with distortion O(log n) [2, 9], this yields an O(log n)-approximation for TM-MFL in general graphs in pseudo-polynomial time...

    Zachary Friggstadet al. Minimizing Movement in Mobile Facility Location Problems

    • ...Probabilistic tree embeddings were introduced by Bartal [2], who showed that any metric can be approximated by a distribution over dominating tree metrics with distortion O(log 2 n). The bound was improved to O(log n log log n) in [3, 5] and to O(log n) in [12]...

    Maleq Khanet al. Efficient distributed approximation algorithms via probabilistic tree ...

    • ...The probabilistic embedding of [7] (and later improvements in [8, 22, 9]) provide in particular embeddings into L1 and serve as the first use of probabilistic partitions in the context of embeddings into normed spaces...

    Ittai Abrahamet al. Advances in metric embedding theory

    • ...(Notice that this problem generalizes 0-Extension by allowing an arbitrary assignment cost function c.) Motivated by applications to segmentation problems in computer vision, this problem was introduced by Kleinberg and Tardos [17], who proposed an approximation algorithm based on the approximate representation, due to Bartal [3], of (T, d) as a combination of dominating tree metrics...

    Howard J. Karloffet al. On earthmover distance, metric labeling, and 0-extension

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