@inproceedings{d486d67bc11c48b5923e2933e20da8db,

title = "On low dimensional local embeddings",

abstract = "We study the problem of embedding metric spaces into low dimensional ℓp spaces while faithfully preserving distances from each point to its k nearest neighbors. We show that any metric space can be embedded into ℓpO(ep log2 k) with k-local distortion of O((log k)/p). We also show that any ultrametric can be embedded into ℓpO(log k)/c3 with k-local distortion 1 + ∈. Our embedding results have immediate applications to local Distance Oracles. We show how to preprocess a graph in polynomial time to obtain a data structure of O(nk1/t log2 k) bits, such that distance queries from any node to its k nearest neighbors can be answered with stretch O(t).",

author = "Ittai Abraham and Yair Bartal and Ofer Neiman",

year = "2009",

doi = "10.1137/1.9781611973068.95",

language = "American English",

isbn = "9780898716801",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery (ACM)",

pages = "875--884",

booktitle = "Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms",

address = "United States",

note = "20th Annual ACM-SIAM Symposium on Discrete Algorithms ; Conference date: 04-01-2009 Through 06-01-2009",

}