Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion

Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion (2007)

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by Ittai Abraham , Yair Bartal , Ofer Neiman

Venue:	In SODA ’07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Citations:	8 - 3 self

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@INPROCEEDINGS{Abraham07embeddingmetrics,
    author = {Ittai Abraham and Yair Bartal and Ofer Neiman},
    title = {Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion},
    booktitle = {In SODA ’07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms},
    year = {2007},
    pages = {502--511}
}

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Abstract

Citations

291	Probabilistic approximations of metric spaces and its algorithmic applications - Bartal - 1996
222	On approximating arbitrary metrices by tree metrics - Bartal - 1998
216	A tight bound on approximating arbitrary metrics by tree metrics - Fakcharoenphol, Rao, et al. - 2003
101	Algorithmic applications of low-distortion geometric embeddings - Indyk - 2001
99	Big-Bang Simulation for Embedding Network Distances - Shavitt, Tankel
91	A Graph Theoretic Game and Its Application to the K-Server Problem - Alon, Karp, et al. - 1995
75	Fast construction of nets in low dimensional metrics, and their applications - Har-Peled, Mendel
70	Properties of embedding methods for similarity searching in metric spaces - Hjaltason, Samet - 2003
65	Triangulation and embedding using small sets of beacons - Kleinberg, Slivkins, et al. - 2004
57	On metric ramsey-type phenomena - Bartal, Linial, et al.
49	Lower-stretch spanning trees - Elkin, Emek, et al. - 2005
37	A Polynomial Time Approximation Scheme for Minimum Routing Cost Spanning Trees - Wu, Lancia, et al. - 1998
34	Lower bounds on the distortion of embedding finite metric spaces in graphs - Rabinovich, Raz - 1998
21	Advances in metric embedding theory - Abraham, Bartal, et al. - 2006
20	Contractive Embedding Methods for Similarity Searching - Hjaltason, Samet - 2000
17	Ramsey-type theorems for metric spaces with applications to online problems - Bartal, Bollobás, et al. - 2002
14	Database indexing methods for 3D hand pose estimation - Athitsos, Sclaroff - 2003
12	Aleksandrs Slivkins. Metric embeddings with relaxed guarantees - Abraham, Bartal, et al. - 2005
12	Multi-embeddings and path-approximation of metric spaces - Bartal, Mendel - 2003
10	Graph decomposition lemmas and their role in metric embedding methods - Bartal - 2004
6	B.Westover, “Detecting protein sequence conservation via metric embeddings - Halperin, Buhler, et al. - 2003
6	Cofe: A scalable method for feature extraction from complex objects - Hristescu, Farach-Colton - 2000
1	2rad(T[Fim(x)]) m=1 ≤ 4c ′ �ℓ−1 m=1 (8/5) m + 4c ′ L� m=ℓ EZh [Pr[Cm \| Z(Zh)] \| Z(X)](8/5) m ≤ 4c ′ (5/3)(8/5) ℓ + 2 12 c · c - Pr
1	On low dimensional Lipschitz embeddings of ultrametrics - Bartal, Mendel - 2002
1	2rad(T [Fim (x)]) m=1 ≤ 4c ′ �ℓ−1 m=1 (8/5) m + 4c ′ L� m=ℓ EZh [Pr[Cm \| Z(Zh)] \| Z(X)] (8/5) m ≤ 4c ′ (5/3)(8/5) ℓ + 2 12 c · c - Pr