Homework 1 - 236779 Nir
نویسنده
چکیده
Ci,hi(at)+ = si(at) • Query: Given a ∈ Σ, return f̂a := mediani=1..u{Ci,hi(a)si(a)} As usual, let fa = |{i : ai = a}| (the frequency of symbol a). For simplicity, you can assume that the stream is determined and fixed ahead of time, then you initialize your algorithm (by randomly choosing the hash functions), ond only then you view the stream. Let TOPk ⊆ Σ denote the set of top-k heavy hitters in the stream (the symbols whose frequency is among the top k). Answer the following questions:
منابع مشابه
Homework 2 Foundations of Algorithms for Massive Datasets ( 236779 ) Fall 2015
Small coherence (or, incoherence) has nice properties as we shall see now. Assume A has coherence μ < 1. Prove that for all s < 1/μ, A has RIP with parameters s, δ = sμ. Hint: For s-sparse x, write down ‖Ax‖ = (Ax)Ax using inner products of columns of A. Note: There exist deterministic constructions of k×d matrices with incoherence ∼ 1/ √ k, which by the above imply RIP with parameters s = √ k,...
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