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REPORTS > KEYWORD > SMOOTHED ANALYSIS:
Reports tagged with Smoothed Analysis:
TR05-063 | 24th June 2005
Bodo Manthey, Rüdiger Reischuk

#### Smoothed Analysis of the Height of Binary Search Trees

Revisions: 2

Binary search trees are one of the most fundamental data structures. While the
height of such a tree may be linear in the worst case, the average height with
respect to the uniform distribution is only logarithmic. The exact value is one
of the best studied problems in average case ... more >>>

TR06-023 | 7th February 2006
Xi Chen, Xiaotie Deng, Shang-Hua Teng

By proving that the problem of computing a $1/n^{\Theta(1)}$-approximate Nash equilibrium remains \textbf{PPAD}-complete, we show that the BIMATRIX game is not likely to have a fully polynomial-time approximation scheme. In other words, no algorithm with time polynomial in $n$ and $1/\epsilon$ can compute an $\epsilon$-approximate Nash equilibrium of an $n\times ... more >>> TR07-039 | 27th March 2007 Bodo Manthey, Till Tantau #### Smoothed Analysis of Binary Search Trees and Quicksort Under Additive Noise Revisions: 1 Binary search trees are a fundamental data structure and their height plays a key role in the analysis of divide-and-conquer algorithms like quicksort. Their worst-case height is linear; their average height, whose exact value is one of the best-studied problems in average-case complexity, is logarithmic. We analyze their smoothed height ... more >>> TR13-008 | 7th January 2013 Adam Klivans, Raghu Meka #### Moment-Matching Polynomials We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem and deviate significantly from known Fourier-based methods, which require the underlying distribution to have some product ... more >>> TR21-179 | 8th December 2021 tatsuie tsukiji #### Smoothed Complexity of Learning Disjunctive Normal Forms, Inverting Fourier Transforms, and Verifying Small Circuits Comments: 1 This paper aims to derandomize the following problems in the smoothed analysis of Spielman and Teng. Learn Disjunctive Normal Form (DNF), invert Fourier Transforms (FT), and verify small circuits' unsatisfiability. Learning algorithms must predict a future observation from the only$m$i.i.d. samples of a fixed but unknown joint-distribution$P(G(x),y)\$ ... more >>>

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