16 Search Results for "Yin, Yitong"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.46
Efficient Parallel Ising Samplers via Localization Schemes

Authors: Xiaoyu Chen, Hongyang Liu, Yitong Yin, and Xinyuan Zhang

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

Abstract
We introduce efficient parallel algorithms for sampling from the Gibbs distribution and estimating the partition function of Ising models. These algorithms achieve parallel efficiency, with polylogarithmic depth and polynomial total work, and are applicable to Ising models in the following regimes: (1) Ferromagnetic Ising models with external fields; (2) Ising models with interaction matrix J of operator norm ‖J‖₂ < 1. Our parallel Gibbs sampling approaches are based on localization schemes, which have proven highly effective in establishing rapid mixing of Gibbs sampling. In this work, we employ two such localization schemes to obtain efficient parallel Ising samplers: the field dynamics induced by negative-field localization, and restricted Gaussian dynamics induced by stochastic localization. This shows that localization schemes are powerful tools, not only for achieving rapid mixing but also for the efficient parallelization of Gibbs sampling.
Cite as

Xiaoyu Chen, Hongyang Liu, Yitong Yin, and Xinyuan Zhang. Efficient Parallel Ising Samplers via Localization Schemes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 46:1-46:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.46,
  author =	{Chen, Xiaoyu and Liu, Hongyang and Yin, Yitong and Zhang, Xinyuan},
  title =	{{Efficient Parallel Ising Samplers via Localization Schemes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{46:1--46:22},
  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.2025.46},
  URN =		{urn:nbn:de:0030-drops-244129},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.46},
  annote =	{Keywords: Localization scheme, parallel sampling, Ising model}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.68
Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree

Authors: Xiaoyu Chen and Weiming Feng

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

Abstract
We develop a new framework to prove the mixing or relaxation time for the Glauber dynamics on spin systems with unbounded degree. It works for general spin systems including both 2-spin and multi-spin systems. As applications for this approach: - We prove the optimal O(n) relaxation time for the Glauber dynamics of random q-list-coloring on an n-vertices triangle-tree graph with maximum degree Δ such that q/Δ > α^⋆, where α^⋆ ≈ 1.763 is the unique positive solution of the equation α = exp(1/α). This improves the n^{1+o(1)} relaxation time for Glauber dynamics obtained by the previous work of Jain, Pham, and Vuong (2022). Besides, our framework can also give a near-linear time sampling algorithm under the same condition. - We prove the optimal O(n) relaxation time and near-optimal Õ(n) mixing time for the Glauber dynamics on hardcore models with parameter λ in balanced bipartite graphs such that λ < λ_c(Δ_L) for the max degree Δ_L in left part and the max degree Δ_R of right part satisfies Δ_R = O(Δ_L). This improves the previous result by Chen, Liu, and Yin (2023). At the heart of our proof is the notion of coupling independence which allows us to consider multiple vertices as a huge single vertex with exponentially large domain and do a "coarse-grained" local-to-global argument on spin systems. The technique works for general (multi) spin systems and helps us obtain some new comparison results for Glauber dynamics.
Cite as

Xiaoyu Chen and Weiming Feng. Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.68,
  author =	{Chen, Xiaoyu and Feng, Weiming},
  title =	{{Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{68:1--68:17},
  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.2025.68},
  URN =		{urn:nbn:de:0030-drops-244345},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.68},
  annote =	{Keywords: coupling independence, Glauber dynamics, mixing times, relaxation times, spin systems}
}
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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.51
Improved Mixing of Critical Hardcore Model

Authors: Zongchen Chen and Tianhui Jiang

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

Abstract
The hardcore model is one of the most classic and widely studied examples of undirected graphical models. Given a graph G, the hardcore model describes a Gibbs distribution of λ-weighted independent sets of G. In the last two decades, a beautiful computational phase transition has been established at a precise threshold λ_c(Δ) where Δ denotes the maximum degree, where the task of sampling independent sets transitions from polynomial-time solvable to computationally intractable. We study the critical hardcore model where λ = λ_c(Δ) and show that the Glauber dynamics, a simple yet popular Markov chain algorithm, mixes in Õ(n^{7.44 + O(1/Δ)}) time on any n-vertex graph of maximum degree Δ ≥ 3, significantly improving the previous upper bound Õ(n^{12.88 + O(1/Δ)}) by the recent work [Chen et al., 2024]. The core property we establish in this work is that the critical hardcore model is O(√n)-spectrally independent, improving the trivial bound of n and matching the critical behavior of the Ising model. Our proof approach utilizes an online decision-making framework to study a site percolation model on the infinite (Δ-1)-ary tree, which can be interesting by itself.
Cite as

Zongchen Chen and Tianhui Jiang. Improved Mixing of Critical Hardcore Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 51:1-51:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.51,
  author =	{Chen, Zongchen and Jiang, Tianhui},
  title =	{{Improved Mixing of Critical Hardcore Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{51:1--51:22},
  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.2025.51},
  URN =		{urn:nbn:de:0030-drops-244176},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.51},
  annote =	{Keywords: Hardcore model, Phase transition, Glauber dynamics, Spectral independence, Online decision making, Site percolation}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.40
An Efficient and Uniform CSP Solution Generator Generator

Authors: Ghiles Ziat and Martin Pépin

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Constraint-based random testing is a powerful technique which aims at generating random test cases to verify functional properties of a program. Its objective is to determine whether a function satisfies a given property for every possible input. This approach requires firstly defining the property to satisfy, then secondly to provide a "generator of inputs" able to feed the program with the inputs generated. Besides, function inputs often need to satisfy certain constraints to ensure the function operates correctly, which makes the crafting of such a generator a hard task. In this paper, we are interested in the problem of manufacturing a uniform and efficient generator for the solutions of a CSP. In order to do that, we propose a specialized solving method that produces a well-suited representation for random sampling. Our solving method employs a dedicated propagation scheme based on the hypergraph representation of a CSP, and a custom split heuristic called birdge-first that emphasizes the interests of our propagation scheme. The generators we build are general enough to handle a wide range of use-cases. They are moreover uniform by construction, iterative and self-improving. We present a prototype built upon the AbSolute constraint solving library and demonstrate its performances on several realistic examples.
Cite as

Ghiles Ziat and Martin Pépin. An Efficient and Uniform CSP Solution Generator Generator. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ziat_et_al:LIPIcs.CP.2025.40,
  author =	{Ziat, Ghiles and P\'{e}pin, Martin},
  title =	{{An Efficient and Uniform CSP Solution Generator Generator}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.40},
  URN =		{urn:nbn:de:0030-drops-239010},
  doi =		{10.4230/LIPIcs.CP.2025.40},
  annote =	{Keywords: Constraint Programming, Property-based Testing}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.13
Random Local Access for Sampling k-SAT Solutions

Authors: Dingding Dong and Nitya Mani

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
We present a sublinear time algorithm that gives random local access to the uniform distribution over satisfying assignments to an arbitrary k-SAT formula Φ, at exponential clause density. Our algorithm provides memory-less query access to variable assignments, such that the output variable assignments consistently emulate a single global satisfying assignment whose law is close to the uniform distribution over satisfying assignments to Φ. Random local access and related models have been studied for a wide variety of natural Gibbs distributions and random graphical processes. Here, we establish feasibility of random local access models for one of the most canonical such sample spaces, the set of satisfying assignments to a k-SAT formula. Our algorithm proceeds by leveraging the local uniformity of the uniform distribution over satisfying assignments to Φ. We randomly partition the variables into two subsets, so that each clause has sufficiently many variables from each set to preserve local uniformity. We then sample some variables by simulating a systematic scan Glauber dynamics backward in time, greedily constructing the necessary intermediate steps. We sample the other variables by first conducting a search for a polylogarithmic-sized local component, which we iteratively grow to identify a small subformula from which we can efficiently sample using the appropriate marginal distribution. This two-pronged approach enables us to sample individual variable assignments without constructing a full solution.
Cite as

Dingding Dong and Nitya Mani. Random Local Access for Sampling k-SAT Solutions. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dong_et_al:LIPIcs.SAT.2025.13,
  author =	{Dong, Dingding and Mani, Nitya},
  title =	{{Random Local Access for Sampling k-SAT Solutions}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{13:1--13:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.13},
  URN =		{urn:nbn:de:0030-drops-237474},
  doi =		{10.4230/LIPIcs.SAT.2025.13},
  annote =	{Keywords: sublinear time algorithms, random generation, k-SAT, local computation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.83
Low-Temperature Sampling on Sparse Random Graphs

Authors: Andreas Galanis, Leslie Ann Goldberg, and Paulina Smolarova

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from the ferromagnetic q-state Potts model. Low-temperature sampling is computationally intractable for general graphs, but recent advances based on the polymer method have made significant progress for graph families that exhibit certain expansion properties that reinforce the correlations, including for example expanders, lattices and dense graphs. One of the most natural graph classes that has so far escaped this algorithmic framework is the class of sparse Erdős-Rényi random graphs whose expansion only manifests for sufficiently large subsets of vertices; small sets of vertices on the other hand have vanishing expansion which makes them behave independently from the bulk of the graph and therefore weakens the correlations. At a more technical level, the expansion of small sets is crucial for establishing the Kotecky-Priess condition which underpins the applicability of the framework. Our main contribution is to develop the polymer method in the low-temperature regime for sparse random graphs. As our running example, we use the Potts and random-cluster models on G(n,d/n) for d = Θ(1), where we show a polynomial-time sampling algorithm for all sufficiently large q and d, at all temperatures. Our approach applies more generally for models that are monotone. Key to our result is a simple polymer definition that blends easily with the connectivity properties of the graph and allows us to show that polymers have size at most O(log n).
Cite as

Andreas Galanis, Leslie Ann Goldberg, and Paulina Smolarova. Low-Temperature Sampling on Sparse Random Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 83:1-83:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galanis_et_al:LIPIcs.ICALP.2025.83,
  author =	{Galanis, Andreas and Goldberg, Leslie Ann and Smolarova, Paulina},
  title =	{{Low-Temperature Sampling on Sparse Random Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{83:1--83:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.83},
  URN =		{urn:nbn:de:0030-drops-234606},
  doi =		{10.4230/LIPIcs.ICALP.2025.83},
  annote =	{Keywords: approximate counting, Glauber dynamics, random cluster model, approximate sampling, Erd\H{o}s-R\'{e}nyi Graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.84
One-Shot Learning for k-SAT

Authors: Andreas Galanis, Leslie Ann Goldberg, and Xusheng Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Consider a k-SAT formula Φ where every variable appears at most d times, and let σ be a satisfying assignment of Φ sampled proportionally to e^{β m(σ)} where m(σ) is the number of variables set to true and β is a real parameter. Given Φ and σ, can we learn the value of β efficiently? This problem falls into a recent line of works about single-sample ("one-shot") learning of Markov random fields. The k-SAT setting we consider here was recently studied by Galanis, Kandiros, and Kalavasis (SODA'24) where they showed that single-sample learning is possible when roughly d ≤ 2^{k/6.45} and impossible when d ≥ (k+1) 2^{k-1}. Crucially, for their impossibility results they used the existence of unsatisfiable instances which, aside from the gap in d, left open the question of whether the feasibility threshold for one-shot learning is dictated by the satisfiability threshold of k-SAT formulas of bounded degree. Our main contribution is to answer this question negatively. We show that one-shot learning for k-SAT is infeasible well below the satisfiability threshold; in fact, we obtain impossibility results for degrees d as low as k² when β is sufficiently large, and bootstrap this to small values of β when d scales exponentially with k, via a probabilistic construction. On the positive side, we simplify the analysis of the learning algorithm and obtain significantly stronger bounds on d in terms of β. In particular, for the uniform case β → 0 that has been studied extensively in the sampling literature, our analysis shows that learning is possible under the condition d≲ 2^{k/2}. This is nearly optimal (up to constant factors) in the sense that it is known that sampling a uniformly-distributed satisfying assignment is NP-hard for d≳ 2^{k/2}.
Cite as

Andreas Galanis, Leslie Ann Goldberg, and Xusheng Zhang. One-Shot Learning for k-SAT. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 84:1-84:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galanis_et_al:LIPIcs.ICALP.2025.84,
  author =	{Galanis, Andreas and Goldberg, Leslie Ann and Zhang, Xusheng},
  title =	{{One-Shot Learning for k-SAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{84:1--84:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.84},
  URN =		{urn:nbn:de:0030-drops-234610},
  doi =		{10.4230/LIPIcs.ICALP.2025.84},
  annote =	{Keywords: Computational Learning Theory, k-SAT, Maximum likelihood estimation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.24
Sampling List Packings

Authors: Evan Camrud, Ewan Davies, Alex Karduna, and Holden Lee

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We initiate the study of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted substantial attention. For list packing the setup is similar, but we seek a full decomposition of the lists of colors into pairwise-disjoint proper list colorings. The existence of a list packing implies the existence of a list coloring, but the converse is false. Recent works on list packing have focused on existence or extremal results of on the number of list packings, but here we turn to the algorithmic aspects of counting and sampling. In graphs of maximum degree Δ and when the number of colors is at least Ω(Δ²), we give a fully polynomial-time randomized approximation scheme (FPRAS) based on rapid mixing of a natural Markov chain (the Glauber dynamics) which we analyze with the path coupling technique. Some motivation for our work is the investigation of an atypical spin system, one where the number of spins for each vertex is much larger than the graph degree.
Cite as

Evan Camrud, Ewan Davies, Alex Karduna, and Holden Lee. Sampling List Packings. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{camrud_et_al:LIPIcs.ITCS.2025.24,
  author =	{Camrud, Evan and Davies, Ewan and Karduna, Alex and Lee, Holden},
  title =	{{Sampling List Packings}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-226528},
  doi =		{10.4230/LIPIcs.ITCS.2025.24},
  annote =	{Keywords: List packing, Graph colouring, Markov chains, Path coupling}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.30
Fast, Fair and Truthful Distributed Stable Matching for Common Preferences

Authors: Juho Hirvonen and Sara Ranjbaran

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair of agents prefer each other over their current matches. The deferred acceptance algorithm of Gale and Shapley solves this problem in polynomial time. Further, it is a mechanism: the proposing side in the algorithm is always incentivised to report their preferences truthfully. The deferred acceptance algorithm has a natural interpretation as a distributed algorithm (and thus a distributed mechanism). However, the algorithm is slow in the worst case and it is known that the stable matching problem cannot be solved efficiently in the distributed setting. In this work we study a natural special case of the stable matching problem where all agents on one of the two sides share common preferences. We show that in this case the deferred acceptance algorithm does yield a fast and truthful distributed mechanism for finding a stable matching. We show how algorithms for sampling random colorings can be used to break ties fairly and extend the results to fractional stable matching.
Cite as

Juho Hirvonen and Sara Ranjbaran. Fast, Fair and Truthful Distributed Stable Matching for Common Preferences. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hirvonen_et_al:LIPIcs.OPODIS.2024.30,
  author =	{Hirvonen, Juho and Ranjbaran, Sara},
  title =	{{Fast, Fair and Truthful Distributed Stable Matching for Common Preferences}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.30},
  URN =		{urn:nbn:de:0030-drops-225666},
  doi =		{10.4230/LIPIcs.OPODIS.2024.30},
  annote =	{Keywords: stable matching, deferred acceptance, local algorithm, mechanism design}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.108
Polynomial-Time Approximation of Zero-Free Partition Functions

Authors: Penghui Yao, Yitong Yin, and Xinyuan Zhang

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

Abstract
Zero-free based algorithms are a major technique for deterministic approximate counting. In Barvinok’s original framework [Barvinok, 2017], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free partition functions. Patel and Regts [Patel and Regts, 2017] later gave a refinement of Barvinok’s framework, which gave a polynomial-time algorithm for a class of zero-free graph polynomials that can be expressed as counting induced subgraphs in bounded-degree graphs. In this paper, we give a polynomial-time algorithm for estimating classical and quantum partition functions specified by local Hamiltonians with bounded maximum degree, assuming a zero-free property for the temperature. Consequently, when the inverse temperature is close enough to zero by a constant gap, we have a polynomial-time approximation algorithm for all such partition functions. Our result is based on a new abstract framework that extends and generalizes the approach of Patel and Regts.
Cite as

Penghui Yao, Yitong Yin, and Xinyuan Zhang. Polynomial-Time Approximation of Zero-Free Partition Functions. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 108:1-108:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{yao_et_al:LIPIcs.ICALP.2022.108,
  author =	{Yao, Penghui and Yin, Yitong and Zhang, Xinyuan},
  title =	{{Polynomial-Time Approximation of Zero-Free Partition Functions}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{108:1--108:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.108},
  URN =		{urn:nbn:de:0030-drops-164494},
  doi =		{10.4230/LIPIcs.ICALP.2022.108},
  annote =	{Keywords: partition function, zero-freeness, local Hamiltonian}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.25
Dynamic Inference in Probabilistic Graphical Models

Authors: Weiming Feng, Kun He, Xiaoming Sun, and Yitong Yin

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Probabilistic graphical models, such as Markov random fields (MRFs), are useful for describing high-dimensional distributions in terms of local dependence structures. The {probabilistic inference} is a fundamental problem related to graphical models, and sampling is a main approach for the problem. In this paper, we study probabilistic inference problems when the graphical model itself is changing dynamically with time. Such dynamic inference problems arise naturally in today’s application, e.g. multivariate time-series data analysis and practical learning procedures. We give a dynamic algorithm for sampling-based probabilistic inferences in MRFs, where each dynamic update can change the underlying graph and all parameters of the MRF simultaneously, as long as the total amount of changes is bounded. More precisely, suppose that the MRF has n variables and polylogarithmic-bounded maximum degree, and N(n) independent samples are sufficient for the inference for a polynomial function N(⋅). Our algorithm dynamically maintains an answer to the inference problem using Õ(n N(n)) space cost, and Õ(N(n) + n) incremental time cost upon each update to the MRF, as long as the Dobrushin-Shlosman condition is satisfied by the MRFs. This well-known condition has long been used for guaranteeing the efficiency of Markov chain Monte Carlo (MCMC) sampling in the traditional static setting. Compared to the static case, which requires Ω(n N(n)) time cost for redrawing all N(n) samples whenever the MRF changes, our dynamic algorithm gives a 𝛺^~(min{n, N(n)})-factor speedup. Our approach relies on a novel dynamic sampling technique, which transforms local Markov chains (a.k.a. single-site dynamics) to dynamic sampling algorithms, and an "algorithmic Lipschitz" condition that we establish for sampling from graphical models, namely, when the MRF changes by a small difference, samples can be modified to reflect the new distribution, with cost proportional to the difference on MRF.
Cite as

Weiming Feng, Kun He, Xiaoming Sun, and Yitong Yin. Dynamic Inference in Probabilistic Graphical Models. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{feng_et_al:LIPIcs.ITCS.2021.25,
  author =	{Feng, Weiming and He, Kun and Sun, Xiaoming and Yin, Yitong},
  title =	{{Dynamic Inference in Probabilistic Graphical Models}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.25},
  URN =		{urn:nbn:de:0030-drops-135643},
  doi =		{10.4230/LIPIcs.ITCS.2021.25},
  annote =	{Keywords: Dynamic inference, probabilistic graphical model, Gibbs sampling, Markov random filed}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.79
Succinct Filters for Sets of Unknown Sizes

Authors: Mingmou Liu, Yitong Yin, and Huacheng Yu

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

Abstract
The membership problem asks to maintain a set S ⊆ [u], supporting insertions and membership queries, i.e., testing if a given element is in the set. A data structure that computes exact answers is called a dictionary. When a (small) false positive rate ε is allowed, the data structure is called a filter. The space usages of the standard dictionaries or filters usually depend on the upper bound on the size of S, while the actual set can be much smaller. Pagh, Segev and Wieder [Pagh et al., 2013] were the first to study filters with varying space usage based on the current |S|. They showed in order to match the space with the current set size n = |S|, any filter data structure must use (1-o(1))n(log(1/ε)+(1-O(ε))log log n) bits, in contrast to the well-known lower bound of N log(1/ε) bits, where N is an upper bound on |S|. They also presented a data structure with almost optimal space of (1+o(1))n(log(1/ε)+O(log log n)) bits provided that n > u^0.001, with expected amortized constant insertion time and worst-case constant lookup time. In this work, we present a filter data structure with improvements in two aspects: - it has constant worst-case time for all insertions and lookups with high probability; - it uses space (1+o(1))n(log (1/ε)+log log n) bits when n > u^0.001, achieving optimal leading constant for all ε = o(1). We also present a dictionary that uses (1+o(1))nlog(u/n) bits of space, matching the optimal space in terms of the current size, and performs all operations in constant time with high probability.
Cite as

Mingmou Liu, Yitong Yin, and Huacheng Yu. Succinct Filters for Sets of Unknown Sizes. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{liu_et_al:LIPIcs.ICALP.2020.79,
  author =	{Liu, Mingmou and Yin, Yitong and Yu, Huacheng},
  title =	{{Succinct Filters for Sets of Unknown Sizes}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{79:1--79:19},
  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.2020.79},
  URN =		{urn:nbn:de:0030-drops-124867},
  doi =		{10.4230/LIPIcs.ICALP.2020.79},
  annote =	{Keywords: Bloom filters, Data structures, Approximate set membership, Dictionaries}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.46
Counting Hypergraph Matchings up to Uniqueness Threshold

Authors: Renjie Song, Yitong Yin, and Jinman Zhao

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter lambda, each matching M is assigned a weight lambda^{|M|}. The counting problem is formulated as computing a partition function that gives the sum of the weights of all matchings in a hypergraph. This problem unifies two extensively studied statistical physics models in approximate counting: the hardcore model (graph independent sets) and the monomer-dimer model (graph matchings). For this model, the critical activity lambda_c= (d^d)/(k (d-1)^{d+1}) is the threshold for the uniqueness of Gibbs measures on the infinite (d+1)-uniform (k+1)-regular hypertree. Consider hypergraphs of maximum degree at most k+1 and maximum size of hyperedges at most d+1. We show that when lambda < lambda_c, there is an FPTAS for computing the partition function; and when lambda = lambda_c, there is a PTAS for computing the log-partition function. These algorithms are based on the decay of correlation (strong spatial mixing) property of Gibbs distributions. When lambda > 2lambda_c, there is no PRAS for the partition function or the log-partition function unless NP=RP. Towards obtaining a sharp transition of computational complexity of approximate counting, we study the local convergence from a sequence of finite hypergraphs to the infinite lattice with specified symmetry. We show a surprising connection between the local convergence and the reversibility of a natural random walk. This leads us to a barrier for the hardness result: The non-uniqueness of infinite Gibbs measure is not realizable by any finite gadgets.
Cite as

Renjie Song, Yitong Yin, and Jinman Zhao. Counting Hypergraph Matchings up to Uniqueness Threshold. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 46:1-46:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{song_et_al:LIPIcs.APPROX-RANDOM.2016.46,
  author =	{Song, Renjie and Yin, Yitong and Zhao, Jinman},
  title =	{{Counting Hypergraph Matchings up to Uniqueness Threshold}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{46:1--46:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.46},
  URN =		{urn:nbn:de:0030-drops-66690},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.46},
  annote =	{Keywords: approximate counting; phase transition; spatial mixing}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.47
Sampling in Potts Model on Sparse Random Graphs

Authors: Yitong Yin and Chihao Zhang

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
We study the problem of sampling almost uniform proper q-colorings in sparse Erdos-Renyi random graphs G(n,d/n), a research initiated by Dyer, Flaxman, Frieze and Vigoda [Dyer et al., RANDOM STRUCT ALGOR, 2006]. We obtain a fully polynomial time almost uniform sampler (FPAUS) for the problem provided q>3d+4, improving the current best bound q>5.5d [Efthymiou, SODA, 2014]. Our sampling algorithm works for more generalized models and broader family of sparse graphs. It is an efficient sampler (in the same sense of FPAUS) for anti-ferromagnetic Potts model with activity 0<=b<1 on G(n,d/n) provided q>3(1-b)d+4. We further identify a family of sparse graphs to which all these results can be extended. This family of graphs is characterized by the notion of contraction function, which is a new measure of the average degree in graphs.
Cite as

Yitong Yin and Chihao Zhang. Sampling in Potts Model on Sparse Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{yin_et_al:LIPIcs.APPROX-RANDOM.2016.47,
  author =	{Yin, Yitong and Zhang, Chihao},
  title =	{{Sampling in Potts Model on Sparse Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.47},
  URN =		{urn:nbn:de:0030-drops-66706},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.47},
  annote =	{Keywords: Potts model, Sampling, Random Graph, Approximation Algorithm}
}
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