All reports by Author Kewen Wu:

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TR24-075
| 13th April 2024
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Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu#### Almost Optimal Time Lower Bound for Approximating Parameterized Clique, CSP, and More, under ETH

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TR24-031
| 22nd February 2024
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Daniel Kane, Anthony Ostuni, Kewen Wu#### Locality Bounds for Sampling Hamming Slices

Revisions: 1

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TR23-188
| 28th November 2023
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Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu#### Parameterized Inapproximability Hypothesis under ETH

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TR21-046
| 22nd March 2021
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Uma Girish, Avishay Tal, Kewen Wu#### Fourier Growth of Parity Decision Trees

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TR19-137
| 24th September 2019
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Shachar Lovett, Kewen Wu, Jiapeng Zhang#### Decision list compression by mild random restrictions

Revisions: 1

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TR19-110
| 23rd August 2019
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Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang#### Improved bounds for the sunflower lemma

Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu

The Parameterized Inapproximability Hypothesis (PIH), which is an analog of the PCP theorem in parameterized complexity, asserts that, there is a constant $\varepsilon> 0$ such that for any computable function $f:\mathbb{N}\to\mathbb{N}$, no $f(k)\cdot n^{O(1)}$-time algorithm can, on input a $k$-variable CSP instance with domain size $n$, find an assignment satisfying ... more >>>

Daniel Kane, Anthony Ostuni, Kewen Wu

Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions.

We build upon and make explicit earlier implicit results of ... more >>>

Venkatesan Guruswami, Bingkai Lin, Xuandi Ren, Yican Sun, Kewen Wu

The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to satisfy an $\varepsilon$ fraction of constraints for some absolute constant $\varepsilon > 0$. PIH plays the role of ... more >>>

Uma Girish, Avishay Tal, Kewen Wu

We prove that for every parity decision tree of depth $d$ on $n$ variables, the sum of absolute values of Fourier coefficients at level $\ell$ is at most $d^{\ell/2} \cdot O(\ell \cdot \log(n))^\ell$.

Our result is nearly tight for small values of $\ell$ and extends a previous Fourier bound ...
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Shachar Lovett, Kewen Wu, Jiapeng Zhang

A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whole term is satisfied by the input. Decision ... more >>>

Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang

A sunflower with $r$ petals is a collection of $r$ sets so that the

intersection of each pair is equal to the intersection of all. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$, with at least about $w^w$ sets, must ...
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