Improved Lower Bounds for Embeddings into $L_1$
نویسندگان
چکیده
منابع مشابه
Improved Lower Bounds for Embeddings into L
We improve upon recent lower bounds on the minimum distortion of embedding certain finite metric spaces into L1. In particular, we show that for every n ≥ 1, there is an n-point metric space of negative type that requires a distortion of Ω(log log n) for such an embedding, implying the same lower bound on the integrality gap of a well-known semidefinite programming relaxation for sparsest cut. ...
متن کاملImproved lower bounds for embeddings into L1
We simplify and improve upon recent lower bounds on the minimum distortion of embedding certain finite metric spaces into L1. In particular, we show that for every n ≥ 1, there is an n-point metric space of negative type that requires a distortion of Ω(log log n) for such an embedding, implying the same lower bound on the integrality gap of a well-known semidefinite programming relaxation for s...
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An oblivious subspace embedding (OSE) for some ε, δ ∈ (0, 1/3) and d ≤ m ≤ n is a distribution D over Rm×n such that for any linear subspace W ⊂ Rn of dimension d, P Π∼D (∀x ∈W, (1− ε)‖x‖2 ≤ ‖Πx‖2 ≤ (1 + ε)‖x‖2) ≥ 1− δ. We prove that any OSE with δ < 1/3 must have m = Ω((d + log(1/δ))/ε2), which is optimal. Furthermore, if every Π in the support of D is sparse, having at most s non-zero entries...
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Article history: Received 24 January 2008 Received in revised form 6 May 2008 Available online 20 May 2008 Communicated by C. Scheideler
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2009
ISSN: 0097-5397,1095-7111
DOI: 10.1137/060660126