@inproceedings{5ab30064f5604de69b6e2f10841e2fc1,

title = "Explicit dimension reduction and its applications",

abstract = "We construct a small set of explicit linear transformations mapping ℝn to ℝt, where t = O (log(γ-1) ε-2), such that the L2 norm of any vector in Rn is distorted by at most 1 ± ε in at least a fraction of 1 - γ of the transformations in the set. Albeit the tradeoff between the size of the set and the success probability is sub-optimal compared with probabilistic arguments, we nevertheless are able to apply our construction to a number of problems. In particular, we use it to construct an ε-sample (or pseudo-random generator) for linear threshold functions on Sn-1, for ε = o(1). We also use it to construct an ε-sample for spherical digons in Sn-1, for ε = o(1). This construction leads to an efficient oblivious derandomization of the Goemans-Williamson MAX CUT algorithm and similar approximation algorithms (i.e., we construct a small set of hyperplanes, such that for any instance we can choose one of them to generate a good solution). Our technique for constructing ε-sample for linear threshold functions on the sphere is considerably different than previous techniques that rely on k-wise independent sample spaces.",

author = "Karnin, {Zohar S.} and Yuval Rabani and Amir Shpilka",

year = "2011",

doi = "10.1109/CCC.2011.20",

language = "American English",

isbn = "9780769544113",

series = "Proceedings of the Annual IEEE Conference on Computational Complexity",

pages = "262--272",

booktitle = "Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011",

note = "26th Annual IEEE Conference on Computational Complexity, CCC 2011 ; Conference date: 08-06-2011 Through 10-06-2011",

}