4 Search Results for "Feng, Weiming"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.54
On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n)

Authors: Charilaos Efthymiou and Weiming Feng

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We study the single-site Glauber dynamics for the fugacity λ, Hard-Core model on the random graph G(n, d/n). We show that for the typical instances of the random graph G(n,d/n) and for fugacity λ < {d^d} / {(d-1)^(d+1)}, the mixing time of Glauber dynamics is n^{1 + O(1/log log n)}. Our result improves on the recent elegant algorithm in [Bezáková, Galanis, Goldberg and Štefankovič; ICALP'22]. The algorithm there is an MCMC-based sampling algorithm, but it is not the Glauber dynamics. Our algorithm here is simpler, as we use the classic Glauber dynamics. Furthermore, the bounds on mixing time we prove are smaller than those in Bezáková et al. paper, hence our algorithm is also faster. The main challenge in our proof is handling vertices with unbounded degrees. We provide stronger results with regard the spectral independence via branching values and show that the our Gibbs distributions satisfy the approximate tensorisation of the entropy. We conjecture that the bounds we have here are optimal for G(n,d/n). As corollary of our analysis for the Hard-Core model, we also get bounds on the mixing time of the Glauber dynamics for the Monomer-Dimer model on G(n,d/n). The bounds we get for this model are slightly better than those we have for the Hard-Core model
Cite as

Charilaos Efthymiou and Weiming Feng. On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{efthymiou_et_al:LIPIcs.ICALP.2023.54,
  author =	{Efthymiou, Charilaos and Feng, Weiming},
  title =	{{On the Mixing Time of Glauber Dynamics for the Hard-Core and Related Models on G(n,d/n)}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.54},
  URN =		{urn:nbn:de:0030-drops-181064},
  doi =		{10.4230/LIPIcs.ICALP.2023.54},
  annote =	{Keywords: spin-system, spin-glass, sparse random (hyper)graph, approximate sampling, efficient 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-dev.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
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-dev.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
DOI: 10.4230/LIPIcs.OPODIS.2020.22
Broadcasting Competitively Against Adaptive Adversary in Multi-Channel Radio Networks

Authors: Haimin Chen and Chaodong Zheng

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
Broadcasting in wireless networks is vulnerable to adversarial jamming. To thwart such behavior, resource competitive analysis is proposed. In this framework, sending, listening, or jamming on one channel for one time slot costs one unit of energy. The adversary can employ arbitrary strategy to disrupt communication, but has a limited energy budget T. The honest nodes, on the other hand, aim to accomplish broadcast while spending only o(T). Previous work has shown, in a C-channels network containing n nodes, for large T values, each node can receive the message in Õ(T/C) time, while spending only Õ(√{T/n}) energy. However, these multi-channel algorithms only work for certain values of n and C, and can only tolerate an oblivious adversary. In this work, we provide new upper and lower bounds for broadcasting in multi-channel radio networks, from the perspective of resource competitiveness. Our algorithms work for arbitrary n,C values, require minimal prior knowledge, and can tolerate a powerful adaptive adversary. More specifically, in our algorithms, for large T values, each node’s runtime is O(T/C), and each node’s energy cost is Õ(√{T/n}). We also complement algorithmic results with lower bounds, proving both the time complexity and the energy complexity of our algorithms are optimal or near-optimal (within a poly-log factor). Our technical contributions lie in using "epidemic broadcast" to achieve time efficiency and resource competitiveness, and employing coupling techniques in the analysis to handle the adaptivity of the adversary. At the lower bound side, we first derive a new energy complexity lower bound for 1-to-1 communication in the multi-channel setting, and then apply simulation and reduction arguments to obtain the desired result.
Cite as

Haimin Chen and Chaodong Zheng. Broadcasting Competitively Against Adaptive Adversary in Multi-Channel Radio Networks. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen_et_al:LIPIcs.OPODIS.2020.22,
  author =	{Chen, Haimin and Zheng, Chaodong},
  title =	{{Broadcasting Competitively Against Adaptive Adversary in Multi-Channel Radio Networks}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.22},
  URN =		{urn:nbn:de:0030-drops-135076},
  doi =		{10.4230/LIPIcs.OPODIS.2020.22},
  annote =	{Keywords: Broadcast, radio networks, resource competitive algorithms}
}
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