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Documents authored by Fei, Yumou

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.31
Unbounded-Width CSPs Are Untestable in a Sublinear Number of Queries

Authors: Yumou Fei

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract
The bounded-degree query model, introduced by Goldreich and Ron (Algorithmica, 2002), is a standard framework in graph property testing and sublinear-time algorithms. Many properties studied in this model, such as bipartiteness and 3-colorability of graphs, can be expressed as satisfiability of constraint satisfaction problems (CSPs). We prove that for the entire class of unbounded-width CSPs, testing satisfiability requires Ω(n) queries in the bounded-degree model. This result unifies and generalizes several previous lower bounds. In particular, it applies to all CSPs that are known to be NP-hard to solve, including k-colorability of 𝓁-uniform hypergraphs for any k,𝓁 ⩾ 2 with (k,𝓁) ≠ (2,2). Our proof combines the techniques from Bogdanov, Obata, and Trevisan (FOCS, 2002), who established the first Ω(n) query lower bound for CSP testing in the bounded-degree model, with known results from universal algebra.
Cite as

Yumou Fei. Unbounded-Width CSPs Are Untestable in a Sublinear Number of Queries. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 31:1-31:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fei:LIPIcs.APPROX/RANDOM.2026.31,
  author =	{Fei, Yumou},
  title =	{{Unbounded-Width CSPs Are Untestable in a Sublinear Number of Queries}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{31:1--31:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.31},
  URN =		{urn:nbn:de:0030-drops-277489},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.31},
  annote =	{Keywords: constraint satisfaction problems, property testing}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.42
On the Spectral Expansion of Monotone Subsets of the Hypercube

Authors: Yumou Fei and Renato Ferreira Pinto Jr.

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset A ⊆ {0,1}ⁿ of density μ(A), the previous best lower bound on the spectral gap, due to Cohen [Cohen, 2016], was γ ≳ μ(A)/n², improving upon the earlier bound γ ≳ μ(A)²/n² established by Ding and Mossel [Ding and Mossel, 2014]. In this paper, we prove the optimal lower bound γ ≳ μ(A)/n. As a corollary, we improve the mixing time upper bound of the random walk on constant-density monotone sets from O(n³), as shown by Ding and Mossel, to O(n²). Along the way, we develop two new inequalities that may be of independent interest: (1) a directed L²-Poincaré inequality on the hypercube, and (2) an "approximate" FKG inequality for monotone sets.
Cite as

Yumou Fei and Renato Ferreira Pinto Jr.. On the Spectral Expansion of Monotone Subsets of the Hypercube. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 42:1-42:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fei_et_al:LIPIcs.APPROX/RANDOM.2025.42,
  author =	{Fei, Yumou and Ferreira Pinto Jr., Renato},
  title =	{{On the Spectral Expansion of Monotone Subsets of the Hypercube}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{42:1--42:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  URN =		{urn:nbn:de:0030-drops-244081},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.42},
  annote =	{Keywords: Random walks, mixing time, FKG inequality, Poincar\'{e} inequality, directed isoperimetry}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.45
Two-State Spin Systems with Negative Interactions

Authors: Yumou Fei, Leslie Ann Goldberg, and Pinyan Lu

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a 2×2 symmetric matrix. Previous results on this problem were restricted either to the case where the matrix has non-negative entries, or to the case where the diagonal entries are equal, i.e. Ising models. In this paper, we study the generalization to arbitrary 2×2 interaction matrices with real entries. We show that in some regions of the parameter space, it’s #P-hard to even determine the sign of the partition function, while in other regions there are fully polynomial approximation schemes for the partition function. Our results reveal several new computational phase transitions.
Cite as

Yumou Fei, Leslie Ann Goldberg, and Pinyan Lu. Two-State Spin Systems with Negative Interactions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fei_et_al:LIPIcs.ITCS.2024.45,
  author =	{Fei, Yumou and Goldberg, Leslie Ann and Lu, Pinyan},
  title =	{{Two-State Spin Systems with Negative Interactions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{45:1--45:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.45},
  URN =		{urn:nbn:de:0030-drops-195739},
  doi =		{10.4230/LIPIcs.ITCS.2024.45},
  annote =	{Keywords: Approximate Counting, Spin Systems, #P-Hardness, Randomized Algorithms}
}

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