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Documents authored by Wang, Jiaheng

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.60
Sink-Free Orientations: A Local Sampler with Applications

Authors: Konrad Anand, Graham Freifeld, Heng Guo, Chunyang Wang, and Jiaheng Wang

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

Abstract
For sink-free orientations in graphs of minimum degree at least 3, we show that there is a deterministic approximate counting algorithm that runs in time O((n^33/ε^32)log(n/ε)), a near-linear time sampling algorithm, and a randomised approximate counting algorithm that runs in time O((n/ε)²log(n/ε)), where n denotes the number of vertices of the input graph and 0 < ε < 1 is the desired accuracy. All three algorithms are based on a local implementation of the sink popping method (Cohn, Pemantle, and Propp, 2002) under the partial rejection sampling framework (Guo, Jerrum, and Liu, 2019).
Cite as

Konrad Anand, Graham Freifeld, Heng Guo, Chunyang Wang, and Jiaheng Wang. Sink-Free Orientations: A Local Sampler with Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2025.60,
  author =	{Anand, Konrad and Freifeld, Graham and Guo, Heng and Wang, Chunyang and Wang, Jiaheng},
  title =	{{Sink-Free Orientations: A Local Sampler with Applications}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{60:1--60:19},
  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.2025.60},
  URN =		{urn:nbn:de:0030-drops-244267},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.60},
  annote =	{Keywords: Sink-free orientations, local sampling, deterministic counting}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.8
Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log n). We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson’s lattice path chain (Wilson 2004).
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang. Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.SoCG.2025.8,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Jerrum, Mark and Wang, Jiaheng},
  title =	{{Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.8},
  URN =		{urn:nbn:de:0030-drops-231607},
  doi =		{10.4230/LIPIcs.SoCG.2025.8},
  annote =	{Keywords: non-crossing spanning trees, Markov chain, mixing time}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.28
Can You Link Up With Treewidth?

Authors: Radu Curticapean, Simon Döring, Daniel Neuen, and Jiaheng Wang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
A central result by Marx [ToC '10] constructs k-vertex graphs H of maximum degree 3 such that n^o(k/log k) time algorithms for detecting colorful H-subgraphs would refute the Exponential-Time Hypothesis (ETH). This result is widely used to obtain almost-tight conditional lower bounds for parameterized problems under ETH. Our first contribution is a new and fully self-contained proof of this result that further simplifies a recent work by Karthik et al. [SOSA 2024]. In our proof, we introduce a novel graph parameter of independent interest, the linkage capacity γ(H), and show that detecting colorful H-subgraphs in time n^o(γ(H)) refutes ETH. Then, we use a simple construction of communication networks credited to Beneš to obtain k-vertex graphs of maximum degree 3 and linkage capacity Ω(k/log k), avoiding arguments involving expander graphs, which were required in previous papers. We also show that every graph H of treewidth t has linkage capacity Ω(t/log t), thus recovering a stronger result shown by Marx [ToC '10] with a simplified proof. Additionally, we obtain new tight lower bounds on the complexity of subgraph detection for certain types of patterns by analyzing their linkage capacity: We prove that almost all k-vertex graphs of polynomial average degree Ω(k^β) for β > 0 have linkage capacity Θ(k), which implies tight lower bounds for finding such patterns H. As an application of these results, we also obtain tight lower bounds for counting small induced subgraphs having a fixed property Φ, improving bounds from, e.g., [Roth et al., FOCS 2020].
Cite as

Radu Curticapean, Simon Döring, Daniel Neuen, and Jiaheng Wang. Can You Link Up With Treewidth?. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 28:1-28:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{curticapean_et_al:LIPIcs.STACS.2025.28,
  author =	{Curticapean, Radu and D\"{o}ring, Simon and Neuen, Daniel and Wang, Jiaheng},
  title =	{{Can You Link Up With Treewidth?}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{28:1--28:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.28},
  URN =		{urn:nbn:de:0030-drops-228534},
  doi =		{10.4230/LIPIcs.STACS.2025.28},
  annote =	{Keywords: subgraph isomorphism, constraint satisfaction problems, linkage capacity, exponential-time hypothesis, parameterized complexity, counting complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.11
Approximate Counting for Spin Systems in Sub-Quadratic Time

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, and Jiaheng Wang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We present two randomised approximate counting algorithms with Õ(n^{2-c}/ε²) running time for some constant c > 0 and accuracy ε: 1) for the hard-core model with fugacity λ on graphs with maximum degree Δ when λ = O(Δ^{-1.5-c₁}) where c₁ = c/(2-2c); 2) for spin systems with strong spatial mixing (SSM) on planar graphs with quadratic growth, such as ℤ². For the hard-core model, Weitz’s algorithm (STOC, 2006) achieves sub-quadratic running time when correlation decays faster than the neighbourhood growth, namely when λ = o(Δ^{-2}). Our first algorithm does not require this property and extends the range where sub-quadratic algorithms exist. Our second algorithm appears to be the first to achieve sub-quadratic running time up to the SSM threshold, albeit on a restricted family of graphs. It also extends to (not necessarily planar) graphs with polynomial growth, such as ℤ^d, but with a running time of the form Õ(n²ε^{-2}/2^{c(log n)^{1/d}}) where d is the exponent of the polynomial growth and c > 0 is some constant.
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, and Jiaheng Wang. Approximate Counting for Spin Systems in Sub-Quadratic Time. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{anand_et_al:LIPIcs.ICALP.2024.11,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Wang, Jiaheng},
  title =	{{Approximate Counting for Spin Systems in Sub-Quadratic Time}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.11},
  URN =		{urn:nbn:de:0030-drops-201543},
  doi =		{10.4230/LIPIcs.ICALP.2024.11},
  annote =	{Keywords: Randomised algorithm, Approximate counting, Spin system, Sub-quadratic algorithm}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.25
Improved Bounds for Randomly Colouring Simple Hypergraphs

Authors: Weiming Feng, Heng Guo, and Jiaheng Wang

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We study the problem of sampling almost uniform proper q-colourings in k-uniform simple hypergraphs with maximum degree Δ. For any δ > 0, if k ≥ 20(1+δ)/δ and q ≥ 100Δ^({2+δ}/{k-4/δ-4}), the running time of our algorithm is Õ(poly(Δ k)⋅ n^1.01), where n is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Vuong, 2021; He, Sun, and Wu, 2021), and does not require Ω(log n) colours unlike the work of Frieze and Anastos (2017).
Cite as

Weiming Feng, Heng Guo, and Jiaheng Wang. Improved Bounds for Randomly Colouring Simple Hypergraphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feng_et_al:LIPIcs.APPROX/RANDOM.2022.25,
  author =	{Feng, Weiming and Guo, Heng and Wang, Jiaheng},
  title =	{{Improved Bounds for Randomly Colouring Simple Hypergraphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.25},
  URN =		{urn:nbn:de:0030-drops-171477},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.25},
  annote =	{Keywords: Approximate counting, Markov chain, Mixing time, Hypergraph colouring}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.100
On the Degree of Boolean Functions as Polynomials over ℤ_m

Authors: Xiaoming Sun, Yuan Sun, Jiaheng Wang, Kewen Wu, Zhiyu Xia, and Yufan Zheng

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Polynomial representations of Boolean functions over various rings such as ℤ and ℤ_m have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of areas including communication complexity, circuit complexity, learning theory, coding theory and so on. For any integer m ≥ 2, each Boolean function has a unique multilinear polynomial representation over ring ℤ_m. The degree of such polynomial is called modulo-m degree, denoted as deg_m(⋅). In this paper, we investigate the lower bound of modulo-m degree of Boolean functions. When m = p^k (k ≥ 1) for some prime p, we give a tight lower bound deg_m(f) ≥ k(p-1) for any non-degenerate function f:{0,1}ⁿ → {0,1}, provided that n is sufficient large. When m contains two different prime factors p and q, we give a nearly optimal lower bound for any symmetric function f:{0,1}ⁿ → {0,1} that deg_m(f) ≥ n/{2+1/(p-1)+1/(q-1)}.
Cite as

Xiaoming Sun, Yuan Sun, Jiaheng Wang, Kewen Wu, Zhiyu Xia, and Yufan Zheng. On the Degree of Boolean Functions as Polynomials over ℤ_m. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sun_et_al:LIPIcs.ICALP.2020.100,
  author =	{Sun, Xiaoming and Sun, Yuan and Wang, Jiaheng and Wu, Kewen and Xia, Zhiyu and Zheng, Yufan},
  title =	{{On the Degree of Boolean Functions as Polynomials over \mathbb{Z}\underlinem}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{100:1--100:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.100},
  URN =		{urn:nbn:de:0030-drops-125070},
  doi =		{10.4230/LIPIcs.ICALP.2020.100},
  annote =	{Keywords: Boolean function, polynomial, modular degree, Ramsey theory}
}
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