6 Search Results for "Huang, Zhiyi"

Document
DOI: 10.4230/LIPIcs.AofA.2024.16
Matching Algorithms in the Sparse Stochastic Block Model

Authors: Anna Brandenberger, Byron Chin, Nathan S. Sheffield, and Divya Shyamal

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
In sparse Erdős-Rényi graphs, it is known that a linear-time algorithm of Karp and Sipser achieves near-optimal matching sizes asymptotically almost surely, giving a law-of-large numbers for the matching numbers of such graphs in terms of solutions to an ODE [Jonathan Aronson et al., 1998]. We provide an extension of this analysis, identifying broad ranges of stochastic block model parameters for which the Karp-Sipser algorithm achieves near-optimal matching sizes, but demonstrating that it cannot perform optimally on general stochastic block model instances. We also consider the problem of constructing a matching online, in which the vertices of one half of a bipartite stochastic block model arrive one-at-a-time, and must be matched as they arrive. We show that, when the expected degrees in all communities are equal, the competitive ratio lower bound of 0.837 found by Mastin and Jaillet for the Erdős-Rényi case [Andrew Mastin and Patrick Jaillet, 2013] is achieved by a simple greedy algorithm, and this competitive ratio is optimal. We then propose and analyze a linear-time online matching algorithm with better performance in general stochastic block models.
Cite as

Anna Brandenberger, Byron Chin, Nathan S. Sheffield, and Divya Shyamal. Matching Algorithms in the Sparse Stochastic Block Model. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{brandenberger_et_al:LIPIcs.AofA.2024.16,
  author =	{Brandenberger, Anna and Chin, Byron and Sheffield, Nathan S. and Shyamal, Divya},
  title =	{{Matching Algorithms in the Sparse Stochastic Block Model}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.16},
  URN =		{urn:nbn:de:0030-drops-204515},
  doi =		{10.4230/LIPIcs.AofA.2024.16},
  annote =	{Keywords: Matching Algorithms, Online Matching, Stochastic Block Model}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.92
Algorithms for the Generalized Poset Sorting Problem

Authors: Shaofeng H.-C. Jiang, Wenqian Wang, Yubo Zhang, and Yuhao Zhang

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

Abstract
We consider a generalized poset sorting problem (GPS), in which we are given a query graph G = (V, E) and an unknown poset 𝒫(V, ≺) that is defined on the same vertex set V, and the goal is to make as few queries as possible to edges in G in order to fully recover 𝒫, where each query (u, v) returns the relation between u, v, i.e., u ≺ v, v ≺ u or u ̸ ∼ v. This generalizes both the poset sorting problem [Faigle et al., SICOMP 88] and the generalized sorting problem [Huang et al., FOCS 11]. We give algorithms with Õ(n poly(k)) query complexity when G is a complete bipartite graph or G is stochastic under the Erdős-Rényi model, where k is the width of the poset, and these generalize [Daskalakis et al., SICOMP 11] which only studies complete graph G. Both results are based on a unified framework that reduces the poset sorting to partitioning the vertices with respect to a given pivot element, which may be of independent interest. Moreover, we also propose novel algorithms to implement this partition oracle. Notably, we suggest a randomized BFS with vertex skipping for the stochastic G, and it yields a nearly-tight bound even for the special case of generalized sorting (for stochastic G) which is comparable to the main result of a recent work [Kuszmaul et al., FOCS 21] but is conceptually different and simplified. Our study of GPS also leads to a new Õ(n^{1 - 1 / (2W)}) competitive ratio for the so-called weighted generalized sorting problem where W is the number of distinct weights in the query graph. This problem was considered as an open question in [Charikar et al., JCSS 02], and our result makes important progress as it yields the first nontrivial sublinear ratio for general weighted query graphs (for any bounded W). We obtain this via an Õ(nk + n^{1.5}) query complexity algorithm for the case where every edge in G is guaranteed to be comparable in the poset, which generalizes a Õ(n^{1.5}) bound for generalized sorting [Huang et al., FOCS 11].
Cite as

Shaofeng H.-C. Jiang, Wenqian Wang, Yubo Zhang, and Yuhao Zhang. Algorithms for the Generalized Poset Sorting Problem. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 92:1-92:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jiang_et_al:LIPIcs.ICALP.2024.92,
  author =	{Jiang, Shaofeng H.-C. and Wang, Wenqian and Zhang, Yubo and Zhang, Yuhao},
  title =	{{Algorithms for the Generalized Poset Sorting Problem}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{92:1--92:15},
  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.2024.92},
  URN =		{urn:nbn:de:0030-drops-202359},
  doi =		{10.4230/LIPIcs.ICALP.2024.92},
  annote =	{Keywords: sorting, poset sorting, generalized sorting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.75
Learning Reserve Prices in Second-Price Auctions

Authors: Yaonan Jin, Pinyan Lu, and Tao Xiao

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for each of all the value distribution families studied in the literature: [0,1]-bounded, [1,H]-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity poly(ε^{-1}) depends on the precision ε ∈ (0, 1), but not on the number of bidders n ≥ 1. Further, in the two bounded-support settings, our learning algorithm allows correlated value distributions. In contrast, the tight sample complexity Θ̃(n) ⋅ poly(ε^{-1}) of Myerson Auction proved by Guo, Huang and Zhang (STOC 2019) has a nearly-linear dependence on n ≥ 1, and holds only for independent value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof.
Cite as

Yaonan Jin, Pinyan Lu, and Tao Xiao. Learning Reserve Prices in Second-Price Auctions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 75:1-75:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jin_et_al:LIPIcs.ITCS.2023.75,
  author =	{Jin, Yaonan and Lu, Pinyan and Xiao, Tao},
  title =	{{Learning Reserve Prices in Second-Price Auctions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{75:1--75:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.75},
  URN =		{urn:nbn:de:0030-drops-175780},
  doi =		{10.4230/LIPIcs.ITCS.2023.75},
  annote =	{Keywords: Revenue Maximization, Sample Complexity, Anonymous Reserve}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.73
Scalable and Jointly Differentially Private Packing

Authors: Zhiyi Huang and Xue Zhu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We introduce an (epsilon, delta)-jointly differentially private algorithm for packing problems. Our algorithm not only achieves the optimal trade-off between the privacy parameter epsilon and the minimum supply requirement (up to logarithmic factors), but is also scalable in the sense that the running time is linear in the number of agents n. Previous algorithms either run in cubic time in n, or require a minimum supply per resource that is sqrt{n} times larger than the best possible.
Cite as

Zhiyi Huang and Xue Zhu. Scalable and Jointly Differentially Private Packing. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 73:1-73:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2019.73,
  author =	{Huang, Zhiyi and Zhu, Xue},
  title =	{{Scalable and Jointly Differentially Private Packing}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{73:1--73:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.73},
  URN =		{urn:nbn:de:0030-drops-106498},
  doi =		{10.4230/LIPIcs.ICALP.2019.73},
  annote =	{Keywords: Joint differential privacy, packing, scalable algorithms}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.14
Online Makespan Minimization: The Power of Restart

Authors: Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of (5 - sqrt{5})/2 ~~ 1.382, matching the lower bound by Chen and Vestjens (ORL 1997). Furthermore, Noga and Seiden note that in many applications one can kill a job and restart it later, and they leave an open problem whether algorithms with restart can obtain better competitive ratios. We resolve this long-standing open problem on the positive end. Our algorithm has a natural rule for killing a processing job: a newly-arrived job replaces the smallest processing job if 1) the new job is larger than other pending jobs, 2) the new job is much larger than the processing one, and 3) the processed portion is small relative to the size of the new job. With appropriate choice of parameters, we show that our algorithm improves the 1.5 competitive ratio for the general case, and the 1.382 competitive ratio for the two-machine case.
Cite as

Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online Makespan Minimization: The Power of Restart. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{huang_et_al:LIPIcs.APPROX-RANDOM.2018.14,
  author =	{Huang, Zhiyi and Kang, Ning and Tang, Zhihao Gavin and Wu, Xiaowei and Zhang, Yuhao},
  title =	{{Online Makespan Minimization: The Power of Restart}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  URN =		{urn:nbn:de:0030-drops-94182},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  annote =	{Keywords: Online Scheduling, Makespan Minimization, Identical Machines}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.79
Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

Authors: Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of the offline vertex, but also on the arrival time of the online vertex. To our knowledge, this is the first competitive ratio strictly larger than 1-1/e for an online bipartite matching problem achieved under the randomized primal-dual framework. Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest offer at its arrival.
Cite as

Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 79:1-79:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2018.79,
  author =	{Huang, Zhiyi and Tang, Zhihao Gavin and Wu, Xiaowei and Zhang, Yuhao},
  title =	{{Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.79},
  URN =		{urn:nbn:de:0030-drops-90830},
  doi =		{10.4230/LIPIcs.ICALP.2018.79},
  annote =	{Keywords: Vertex Weighted, Online Bipartite Matching, Randomized Primal-Dual}
}
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