7 Search Results for "Zhang, Chihao"


Document
Track A: Algorithms, Complexity and Games
A Perfect Sampler for Hypergraph Independent Sets

Authors: Guoliang Qiu, Yanheng Wang, and Chihao Zhang

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


Abstract
The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a similar condition of the asymmetric Lovász local lemma. When specialized to d-regular k-uniform hypergraphs on n vertices, our sampler terminates in expected O(n log n) time provided d ≤ c⋅ 2^{k/2} where c > 0 is a constant, matching the rapid mixing condition for Glauber dynamics in Hermon, Sly and Zhang [Hermon et al., 2019]. The analysis of our algorithm is simple and clean.

Cite as

Guoliang Qiu, Yanheng Wang, and Chihao Zhang. A Perfect Sampler for Hypergraph Independent Sets. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 103:1-103:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{qiu_et_al:LIPIcs.ICALP.2022.103,
  author =	{Qiu, Guoliang and Wang, Yanheng and Zhang, Chihao},
  title =	{{A Perfect Sampler for Hypergraph Independent Sets}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{103:1--103:16},
  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.2022.103},
  URN =		{urn:nbn:de:0030-drops-164442},
  doi =		{10.4230/LIPIcs.ICALP.2022.103},
  annote =	{Keywords: Coupling from the past, Markov chains, Hypergraph independent sets}
}
Document
Domain Sparsification of Discrete Distributions Using Entropic Independence

Authors: Nima Anari, Michał Dereziński, Thuy-Duong Vuong, and Elizabeth Yang

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We present a framework for speeding up the time it takes to sample from discrete distributions μ defined over subsets of size k of a ground set of n elements, in the regime where k is much smaller than n. We show that if one has access to estimates of marginals P_{S∼ μ} {i ∈ S}, then the task of sampling from μ can be reduced to sampling from related distributions ν supported on size k subsets of a ground set of only n^{1-α}⋅ poly(k) elements. Here, 1/α ∈ [1, k] is the parameter of entropic independence for μ. Further, our algorithm only requires sparsified distributions ν that are obtained by applying a sparse (mostly 0) external field to μ, an operation that for many distributions μ of interest, retains algorithmic tractability of sampling from ν. This phenomenon, which we dub domain sparsification, allows us to pay a one-time cost of estimating the marginals of μ, and in return reduce the amortized cost needed to produce many samples from the distribution μ, as is often needed in upstream tasks such as counting and inference. For a wide range of distributions where α = Ω(1), our result reduces the domain size, and as a corollary, the cost-per-sample, by a poly(n) factor. Examples include monomers in a monomer-dimer system, non-symmetric determinantal point processes, and partition-constrained Strongly Rayleigh measures. Our work significantly extends the reach of prior work of Anari and Dereziński who obtained domain sparsification for distributions with a log-concave generating polynomial (corresponding to α = 1). As a corollary of our new analysis techniques, we also obtain a less stringent requirement on the accuracy of marginal estimates even for the case of log-concave polynomials; roughly speaking, we show that constant-factor approximation is enough for domain sparsification, improving over O(1/k) relative error established in prior work.

Cite as

Nima Anari, Michał Dereziński, Thuy-Duong Vuong, and Elizabeth Yang. Domain Sparsification of Discrete Distributions Using Entropic Independence. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{anari_et_al:LIPIcs.ITCS.2022.5,
  author =	{Anari, Nima and Derezi\'{n}ski, Micha{\l} and Vuong, Thuy-Duong and Yang, Elizabeth},
  title =	{{Domain Sparsification of Discrete Distributions Using Entropic Independence}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.5},
  URN =		{urn:nbn:de:0030-drops-156013},
  doi =		{10.4230/LIPIcs.ITCS.2022.5},
  annote =	{Keywords: Domain Sparsification, Markov Chains, Sampling, Entropic Independence}
}
Document
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)


Copy BibTex To Clipboard

@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}
}
Document
FPTAS for Hardcore and Ising Models on Hypergraphs

Authors: Pinyan Lu, Kuan Yang, and Chihao Zhang

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)


Abstract
Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS under a slightly stronger condition.

Cite as

Pinyan Lu, Kuan Yang, and Chihao Zhang. FPTAS for Hardcore and Ising Models on Hypergraphs. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 51:1-51:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


Copy BibTex To Clipboard

@InProceedings{lu_et_al:LIPIcs.STACS.2016.51,
  author =	{Lu, Pinyan and Yang, Kuan and Zhang, Chihao},
  title =	{{FPTAS for Hardcore and Ising Models on Hypergraphs}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.51},
  URN =		{urn:nbn:de:0030-drops-57526},
  doi =		{10.4230/LIPIcs.STACS.2016.51},
  annote =	{Keywords: hard-core model, ising model, hypergraph, spatial mixing, correlation decay}
}
Document
Local Convergence of Random Graph Colorings

Authors: Amin Coja-Oghlan, Charilaos Efthymiou, and Nor Jaafari

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
Let G=G(n,m) be a random graph whose average degree d=2m/n is below the k-colorability threshold. If we sample a k-coloring Sigma of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called condensation threshold d_c, the colors assigned to far away vertices are asymptotically independent [Krzakala et al: PNAS 2007]. We prove this conjecture for k exceeding a certain constant k_0. More generally, we determine the joint distribution of the k-colorings that Sigma induces locally on the bounded-depth neighborhoods of a fixed number of vertices.

Cite as

Amin Coja-Oghlan, Charilaos Efthymiou, and Nor Jaafari. Local Convergence of Random Graph Colorings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 726-737, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Copy BibTex To Clipboard

@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2015.726,
  author =	{Coja-Oghlan, Amin and Efthymiou, Charilaos and Jaafari, Nor},
  title =	{{Local Convergence of Random Graph Colorings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{726--737},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.726},
  URN =		{urn:nbn:de:0030-drops-53321},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.726},
  annote =	{Keywords: Random graph, Galton-Watson tree, phase transitions, graph coloring, Gibbs distribution, convergence}
}
Document
Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees

Authors: Charilaos Efthymiou

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
The broadcasting models on trees arise in many contexts such as discrete mathematics, biology, information theory, statistical physics and computer science. In this work, we consider the k-colouring model. A basic question here is whether the assignment at the root affects the distribution of the colourings at the vertices at distance h from the root. This is the so-called reconstruction problem. For the case where the underlying tree is d -ary it is well known that d/ln(d) is the reconstruction threshold. That is, for k=(1+epsilon)*d/ln(d) we have non-reconstruction while for k=(1-epsilon)*d/ln(d) we have reconstruction. Here, we consider the largely unstudied case where the underlying tree is chosen according to a predefined distribution. In particular, we consider the well-known Galton-Watson trees. The corresponding model arises naturally in many contexts such as the theory of spin-glasses and its applications on random Constraint Satisfaction Problems (rCSP). The study on rCSP focuses on Galton-Watson trees with offspring distribution B(n,d/n), i.e. the binomial with parameters n and d/n, where d is fixed. Here we consider a broader version of the problem, as we assume general offspring distribution which includes B(n,d/n) as a special case. Our approach relates the corresponding bounds for (non)reconstruction to certain concentration properties of the offspring distribution. This allows to derive reconstruction thresholds for a very wide family of offspring distributions, which includes B(n,d/n). A very interesting corollary is that for distributions with expected offspring d, we get reconstruction threshold d/ln(d) under weaker concentration conditions than what we have in B(n,d/n). Furthermore, our reconstruction threshold for the random colorings of Galton-Watson with offspring B(n,d/n), implies the reconstruction threshold for the random colourings of G(n,d/n).

Cite as

Charilaos Efthymiou. Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 756-774, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


Copy BibTex To Clipboard

@InProceedings{efthymiou:LIPIcs.APPROX-RANDOM.2015.756,
  author =	{Efthymiou, Charilaos},
  title =	{{Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{756--774},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.756},
  URN =		{urn:nbn:de:0030-drops-53346},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.756},
  annote =	{Keywords: Random Colouring, Reconstruction Problem, Galton-Watson Tree}
}
Document
The Complexity of Ferromagnetic Two-spin Systems with External Fields

Authors: Jingcheng Liu, Pinyan Lu, and Chihao Zhang

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)


Abstract
We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS) for the special ferromagnetic Ising model with any given uniform external field. Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we allow inconsistent external fields on different nodes. In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard, even if the external field is uniform.

Cite as

Jingcheng Liu, Pinyan Lu, and Chihao Zhang. The Complexity of Ferromagnetic Two-spin Systems with External Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 843-856, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.APPROX-RANDOM.2014.843,
  author =	{Liu, Jingcheng and Lu, Pinyan and Zhang, Chihao},
  title =	{{The Complexity of Ferromagnetic Two-spin Systems with External Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{843--856},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.843},
  URN =		{urn:nbn:de:0030-drops-47428},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.843},
  annote =	{Keywords: Spin System, #BIS-hard, FPRAS}
}
  • Refine by Author
  • 4 Zhang, Chihao
  • 2 Efthymiou, Charilaos
  • 2 Lu, Pinyan
  • 1 Anari, Nima
  • 1 Coja-Oghlan, Amin
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Random walks and Markov chains
  • 1 Theory of computation → Sketching and sampling

  • Refine by Keyword
  • 2 Sampling
  • 1 #BIS-hard
  • 1 Approximation Algorithm
  • 1 Coupling from the past
  • 1 Domain Sparsification
  • Show More...

  • Refine by Type
  • 7 document

  • Refine by Publication Year
  • 2 2015
  • 2 2016
  • 2 2022
  • 1 2014

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail