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Documents authored by Wu, Xinyu

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.97
The SDP Value of Random 2CSPs

Authors: Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over {±1}ⁿ. For each model ℳ, we identify the "high-probability value" s^*_ℳ of the natural SDP relaxation (equivalently, the quantum value). That is, for all ε > 0 we show that the SDP optimum of a random n-variable instance is (when normalized by n) in the range (s^*_ℳ-ε, s^*_ℳ+ε) with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.
Cite as

Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu. The SDP Value of Random 2CSPs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 97:1-97:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{musipatla_et_al:LIPIcs.ICALP.2022.97,
  author =	{Musipatla, Amulya and O'Donnell, Ryan and Schramm, Tselil and Wu, Xinyu},
  title =	{{The SDP Value of Random 2CSPs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{97:1--97:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.97},
  URN =		{urn:nbn:de:0030-drops-164381},
  doi =		{10.4230/LIPIcs.ICALP.2022.97},
  annote =	{Keywords: Random constraint satisfaction problems}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.60
Analyzing XOR-Forrelation Through Stochastic Calculus

Authors: Xinyu Wu

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
In this note we present a simplified analysis of the quantum and classical complexity of the k-XOR Forrelation problem (introduced in the paper of Girish, Raz and Zhan [Uma Girish et al., 2020]) by a stochastic interpretation of the Forrelation distribution.
Cite as

Xinyu Wu. Analyzing XOR-Forrelation Through Stochastic Calculus. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 60:1-60:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{wu:LIPIcs.STACS.2022.60,
  author =	{Wu, Xinyu},
  title =	{{Analyzing XOR-Forrelation Through Stochastic Calculus}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{60:1--60:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.60},
  URN =		{urn:nbn:de:0030-drops-158705},
  doi =		{10.4230/LIPIcs.STACS.2022.60},
  annote =	{Keywords: quantum complexity, Brownian motion}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.34
A Log-Sobolev Inequality for the Multislice, with Applications

Authors: Yuval Filmus, Ryan O'Donnell, and Xinyu Wu

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Let kappa in N_+^l satisfy kappa_1 + *s + kappa_l = n, and let U_kappa denote the multislice of all strings u in [l]^n having exactly kappa_i coordinates equal to i, for all i in [l]. Consider the Markov chain on U_kappa where a step is a random transposition of two coordinates of u. We show that the log-Sobolev constant rho_kappa for the chain satisfies rho_kappa^{-1} <= n * sum_{i=1}^l 1/2 log_2(4n/kappa_i), which is sharp up to constants whenever l is constant. From this, we derive some consequences for small-set expansion and isoperimetry in the multislice, including a KKL Theorem, a Kruskal - Katona Theorem for the multislice, a Friedgut Junta Theorem, and a Nisan - Szegedy Theorem.
Cite as

Yuval Filmus, Ryan O'Donnell, and Xinyu Wu. A Log-Sobolev Inequality for the Multislice, with Applications. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{filmus_et_al:LIPIcs.ITCS.2019.34,
  author =	{Filmus, Yuval and O'Donnell, Ryan and Wu, Xinyu},
  title =	{{A Log-Sobolev Inequality for the Multislice, with Applications}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{34:1--34:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.34},
  URN =		{urn:nbn:de:0030-drops-101279},
  doi =		{10.4230/LIPIcs.ITCS.2019.34},
  annote =	{Keywords: log-Sobolev inequality, small-set expansion, conductance, hypercontractivity, Fourier analysis, representation theory, Markov chains, combinatorics}
}
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