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Documents authored by Yi, Li

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Yi, Li

Document
DOI: 10.4230/OASIcs.iPMVM.2020.1
Development and Validation of Energy Simulation for Additive Manufacturing

Authors: Li Yi and Jan C. Aurich

Published in: OASIcs, Volume 89, 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)

Abstract
Additive manufacturing (AM) is a promising manufacturing technology towards cleaner production systems. Nevertheless, recent studies state that environmental benefits of AM are case-specific and need to be evaluated and confirmed in the design phase. To enable the energy performance evaluation in the design phase, developing convenient tools for energy prediction of AM has been an important research task. Aiming at this problem, this paper presents the research for energy modeling, simulation implementation, and experimental validation of an energy simulation tool of two AM processes: Selective laser melting (SLM) and Fused deposition modeling (FDM). The developed simulation tool can be conveniently used for energy consumption quantification and evaluation during the product and process design for AM.
Cite as

Li Yi and Jan C. Aurich. Development and Validation of Energy Simulation for Additive Manufacturing. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{yi_et_al:OASIcs.iPMVM.2020.1,
  author =	{Yi, Li and Aurich, Jan C.},
  title =	{{Development and Validation of Energy Simulation for Additive Manufacturing}},
  booktitle =	{2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)},
  pages =	{1:1--1:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-183-2},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{89},
  editor =	{Garth, Christoph and Aurich, Jan C. and Linke, Barbara and M\"{u}ller, Ralf and Ravani, Bahram and Weber, Gunther H. and Kirsch, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.iPMVM.2020.1},
  URN =		{urn:nbn:de:0030-drops-137500},
  doi =		{10.4230/OASIcs.iPMVM.2020.1},
  annote =	{Keywords: Additive manufacturing, fused deposition modeling, selective laser melting, energy simulation, eco-design for AM}
}

Li, Yi

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.13
Streaming Algorithms with Large Approximation Factors

Authors: Yi Li, Honghao Lin, David P. Woodruff, and Yuheng Zhang

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

Abstract
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor α to be much larger than 1. Such algorithms can use significantly less memory than the usual setting for which α = 1+ε for an ε ∈ (0,1). We study large approximations for a number of problems in sketching and streaming, assuming that the underlying n-dimensional vector has all coordinates bounded by M throughout the data stream: 1) For the 𝓁_p norm/quasi-norm, 0 < p ≤ 2, we show that obtaining a poly(n)-approximation requires the same amount of memory as obtaining an O(1)-approximation for any M = n^Θ(1), which holds even for randomly ordered streams or for streams in the bounded deletion model. 2) For estimating the 𝓁_p norm, p > 2, we show an upper bound of O(n^{1-2/p} (log n log M)/α²) bits for an α-approximation, and give a matching lower bound for linear sketches. 3) For the 𝓁₂-heavy hitters problem, we show that the known lower bound of Ω(k log nlog M) bits for identifying (1/k)-heavy hitters holds even if we are allowed to output items that are 1/(α k)-heavy, provided the algorithm succeeds with probability 1-O(1/n). We also obtain a lower bound for linear sketches that is tight even for constant failure probability algorithms. 4) For estimating the number 𝓁₀ of distinct elements, we give an n^{1/t}-approximation algorithm using O(tlog log M) bits of space, as well as a lower bound of Ω(t) bits, both excluding the storage of random bits, where n is the dimension of the underlying frequency vector and M is an upper bound on the magnitude of its coordinates. 5) For α-approximation to the Schatten-p norm, we give near-optimal Õ(n^{2-4/p}/α⁴) sketching dimension for every even integer p and every α ≥ 1, while for p not an even integer we obtain near-optimal sketching dimension once α = Ω(n^{1/q-1/p}), where q is the largest even integer less than p. The latter is surprising as it is unknown what the complexity of Schatten-p norm estimation is for constant approximation; we show once the approximation factor is at least n^{1/q-1/p}, we can obtain near-optimal sketching bounds.
Cite as

Yi Li, Honghao Lin, David P. Woodruff, and Yuheng Zhang. Streaming Algorithms with Large Approximation Factors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{li_et_al:LIPIcs.APPROX/RANDOM.2022.13,
  author =	{Li, Yi and Lin, Honghao and Woodruff, David P. and Zhang, Yuheng},
  title =	{{Streaming Algorithms with Large Approximation Factors}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.13},
  URN =		{urn:nbn:de:0030-drops-171354},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.13},
  annote =	{Keywords: streaming algorithms, 𝓁\underlinep norm, heavy hitters, distinct elements}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.35
The Product of Gaussian Matrices Is Close to Gaussian

Authors: Yi Li and David P. Woodruff

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We study the distribution of the matrix product G₁ G₂ ⋯ G_r of r independent Gaussian matrices of various sizes, where G_i is d_{i-1} × d_i, and we denote p = d₀, q = d_r, and require d₁ = d_{r-1}. Here the entries in each G_i are standard normal random variables with mean 0 and variance 1. Such products arise in the study of wireless communication, dynamical systems, and quantum transport, among other places. We show that, provided each d_i, i = 1, …, r, satisfies d_i ≥ C p ⋅ q, where C ≥ C₀ for a constant C₀ > 0 depending on r, then the matrix product G₁ G₂ ⋯ G_r has variation distance at most δ to a p × q matrix G of i.i.d. standard normal random variables with mean 0 and variance ∏_{i = 1}^{r-1} d_i. Here δ → 0 as C → ∞. Moreover, we show a converse for constant r that if d_i < C' max{p,q}^{1/2}min{p,q}^{3/2} for some i, then this total variation distance is at least δ', for an absolute constant δ' > 0 depending on C' and r. This converse is best possible when p = Θ(q).
Cite as

Yi Li and David P. Woodruff. The Product of Gaussian Matrices Is Close to Gaussian. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{li_et_al:LIPIcs.APPROX/RANDOM.2021.35,
  author =	{Li, Yi and Woodruff, David P.},
  title =	{{The Product of Gaussian Matrices Is Close to Gaussian}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{35:1--35:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.35},
  URN =		{urn:nbn:de:0030-drops-147281},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.35},
  annote =	{Keywords: random matrix theory, total variation distance, matrix product}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.39
Geometric Cover with Outliers Removal

Authors: Zhengyang Guo and Yi Li

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We study the problem of partial geometric cover, which asks to find the minimum number of geometric objects (unit squares and unit disks in this work) that cover at least (n-t) of n given planar points, where 0 ≤ t ≤ n/2. When t = 0, the problem is the classical geometric cover problem, for which many existing works adopt a general framework called the shifting strategy. The shifting strategy is a divide and conquer paradigm which partitions the plane into equal-width strips, applies a local algorithm on each strip and then merges the local solutions with only a small loss on the overall approximation ratio. A challenge to extend the shifting strategy to the case of outliers is to determine the number of outliers in each strip. We develop a shifting strategy incorporating the outlier distribution, which runs in O(tn log n) time. We also develop local algorithms on strips for the outliers case, improving the running time over previous algorithms, and consequently obtain approximation algorithms to the partial geometric cover.
Cite as

Zhengyang Guo and Yi Li. Geometric Cover with Outliers Removal. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{guo_et_al:LIPIcs.STACS.2021.39,
  author =	{Guo, Zhengyang and Li, Yi},
  title =	{{Geometric Cover with Outliers Removal}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.39},
  URN =		{urn:nbn:de:0030-drops-136849},
  doi =		{10.4230/LIPIcs.STACS.2021.39},
  annote =	{Keywords: Geometric Cover, Unit Square Cover, Unit Disk Cover, Shifting Strategy, Outliers Detection, Computational Geometry}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.50
Streaming Complexity of SVMs

Authors: Alexandr Andoni, Collin Burns, Yi Li, Sepideh Mahabadi, and David P. Woodruff

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We study the space complexity of solving the bias-regularized SVM problem in the streaming model. In particular, given a data set (x_i,y_i) ∈ ℝ^d× {-1,+1}, the objective function is F_λ(θ,b) = λ/2‖(θ,b)‖₂² + 1/n∑_{i=1}ⁿ max{0,1-y_i(θ^Tx_i+b)} and the goal is to find the parameters that (approximately) minimize this objective. This is a classic supervised learning problem that has drawn lots of attention, including for developing fast algorithms for solving the problem approximately: i.e., for finding (θ,b) such that F_λ(θ,b) ≤ min_{(θ',b')} F_λ(θ',b')+ε. One of the most widely used algorithms for approximately optimizing the SVM objective is Stochastic Gradient Descent (SGD), which requires only O(1/λε) random samples, and which immediately yields a streaming algorithm that uses O(d/λε) space. For related problems, better streaming algorithms are only known for smooth functions, unlike the SVM objective that we focus on in this work. We initiate an investigation of the space complexity for both finding an approximate optimum of this objective, and for the related "point estimation" problem of sketching the data set to evaluate the function value F_λ on any query (θ, b). We show that, for both problems, for dimensions d = 1,2, one can obtain streaming algorithms with space polynomially smaller than 1/λε, which is the complexity of SGD for strongly convex functions like the bias-regularized SVM [Shalev-Shwartz et al., 2007], and which is known to be tight in general, even for d = 1 [Agarwal et al., 2009]. We also prove polynomial lower bounds for both point estimation and optimization. In particular, for point estimation we obtain a tight bound of Θ(1/√{ε}) for d = 1 and a nearly tight lower bound of Ω̃(d/{ε}²) for d = Ω(log(1/ε)). Finally, for optimization, we prove a Ω(1/√{ε}) lower bound for d = Ω(log(1/ε)), and show similar bounds when d is constant.
Cite as

Alexandr Andoni, Collin Burns, Yi Li, Sepideh Mahabadi, and David P. Woodruff. Streaming Complexity of SVMs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{andoni_et_al:LIPIcs.APPROX/RANDOM.2020.50,
  author =	{Andoni, Alexandr and Burns, Collin and Li, Yi and Mahabadi, Sepideh and Woodruff, David P.},
  title =	{{Streaming Complexity of SVMs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{50:1--50:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.50},
  URN =		{urn:nbn:de:0030-drops-126532},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.50},
  annote =	{Keywords: support vector machine, streaming algorithm, space lower bound, sketching algorithm, point estimation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.77
Deterministic Sparse Fourier Transform with an 𝓁_{∞} Guarantee

Authors: Yi Li and Vasileios Nakos

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

Abstract
In this paper we revisit the deterministic version of the Sparse Fourier Transform problem, which asks to read only a few entries of x ∈ ℂⁿ and design a recovery algorithm such that the output of the algorithm approximates x̂, the Discrete Fourier Transform (DFT) of x. The randomized case has been well-understood, while the main work in the deterministic case is that of Merhi et al. (J Fourier Anal Appl 2018), which obtains O(k² log^(-1) k ⋅ log^5.5 n) samples and a similar runtime with the 𝓁₂/𝓁₁ guarantee. We focus on the stronger 𝓁_∞/𝓁₁ guarantee and the closely related problem of incoherent matrices. We list our contributions as follows. 1) We find a deterministic collection of O(k² log n) samples for the 𝓁_∞/𝓁₁ recovery in time O(nk log² n), and a deterministic collection of O(k² log² n) samples for the 𝓁_∞/𝓁₁ sparse recovery in time O(k² log³n). 2) We give new deterministic constructions of incoherent matrices that are row-sampled submatrices of the DFT matrix, via a derandomization of Bernstein’s inequality and bounds on exponential sums considered in analytic number theory. Our first construction matches a previous randomized construction of Nelson, Nguyen and Woodruff (RANDOM'12), where there was no constraint on the form of the incoherent matrix. Our algorithms are nearly sample-optimal, since a lower bound of Ω(k² + k log n) is known, even for the case where the sensing matrix can be arbitrarily designed. A similar lower bound of Ω(k² log n/ log k) is known for incoherent matrices.
Cite as

Yi Li and Vasileios Nakos. Deterministic Sparse Fourier Transform with an 𝓁_{∞} Guarantee. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{li_et_al:LIPIcs.ICALP.2020.77,
  author =	{Li, Yi and Nakos, Vasileios},
  title =	{{Deterministic Sparse Fourier Transform with an 𝓁\underline\{∞\} Guarantee}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{77:1--77:14},
  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.2020.77},
  URN =		{urn:nbn:de:0030-drops-124844},
  doi =		{10.4230/LIPIcs.ICALP.2020.77},
  annote =	{Keywords: Fourier sparse recovery, derandomization, incoherent matrices}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.18
Deterministic Heavy Hitters with Sublinear Query Time

Authors: Yi Li and Vasileios Nakos

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

Abstract
We study the classic problem of finding l_1 heavy hitters in the streaming model. In the general turnstile model, we give the first deterministic sublinear-time sketching algorithm which takes a linear sketch of length O(epsilon^{-2} log n * log^*(epsilon^{-1})), which is only a factor of log^*(epsilon^{-1}) more than the best existing polynomial-time sketching algorithm (Nelson et al., RANDOM '12). Our approach is based on an iterative procedure, where most unrecovered heavy hitters are identified in each iteration. Although this technique has been extensively employed in the related problem of sparse recovery, this is the first time, to the best of our knowledge, that it has been used in the context of heavy hitters. Along the way we also obtain a sublinear time algorithm for the closely related problem of the l_1/l_1 compressed sensing, matching the space usage of previous (super-)linear time algorithms. In the strict turnstile model, we show that the runtime can be improved and the sketching matrix can be made strongly explicit with O(epsilon^{-2}log^3 n/log^3(1/epsilon)) rows.
Cite as

Yi Li and Vasileios Nakos. Deterministic Heavy Hitters with Sublinear Query Time. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{li_et_al:LIPIcs.APPROX-RANDOM.2018.18,
  author =	{Li, Yi and Nakos, Vasileios},
  title =	{{Deterministic Heavy Hitters with Sublinear Query Time}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{18:1--18:18},
  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.2018.18},
  URN =		{urn:nbn:de:0030-drops-94221},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.18},
  annote =	{Keywords: heavy hitters, turnstile model, sketching algorithm, strongly explicit}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.19
On Low-Risk Heavy Hitters and Sparse Recovery Schemes

Authors: Yi Li, Vasileios Nakos, and David P. Woodruff

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

Abstract
We study the heavy hitters and related sparse recovery problems in the low failure probability regime. This regime is not well-understood, and the main previous work on this is by Gilbert et al. (ICALP'13). We recognize an error in their analysis, improve their results, and contribute new sparse recovery algorithms, as well as provide upper and lower bounds for the heavy hitters problem with low failure probability. Our results are summarized as follows: 1) (Heavy Hitters) We study three natural variants for finding heavy hitters in the strict turnstile model, where the variant depends on the quality of the desired output. For the weakest variant, we give a randomized algorithm improving the failure probability analysis of the ubiquitous Count-Min data structure. We also give a new lower bound for deterministic schemes, resolving a question about this variant posed in Question 4 in the IITK Workshop on Algorithms for Data Streams (2006). Under the strongest and well-studied l_{infty}/ l_2 variant, we show that the classical Count-Sketch data structure is optimal for very low failure probabilities, which was previously unknown. 2) (Sparse Recovery Algorithms) For non-adaptive sparse-recovery, we give sublinear-time algorithms with low-failure probability, which improve upon Gilbert et al. (ICALP'13). In the adaptive case, we improve the failure probability from a constant by Indyk et al. (FOCS '11) to e^{-k^{0.99}}, where k is the sparsity parameter. 3) (Optimal Average-Case Sparse Recovery Bounds) We give matching upper and lower bounds in all parameters, including the failure probability, for the measurement complexity of the l_2/l_2 sparse recovery problem in the spiked-covariance model, completely settling its complexity in this model.
Cite as

Yi Li, Vasileios Nakos, and David P. Woodruff. On Low-Risk Heavy Hitters and Sparse Recovery Schemes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 19:1-19:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{li_et_al:LIPIcs.APPROX-RANDOM.2018.19,
  author =	{Li, Yi and Nakos, Vasileios and Woodruff, David P.},
  title =	{{On Low-Risk Heavy Hitters and Sparse Recovery Schemes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{19:1--19:13},
  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.2018.19},
  URN =		{urn:nbn:de:0030-drops-94237},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.19},
  annote =	{Keywords: heavy hitters, sparse recovery, turnstile model, spike covariance model, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.60
Embeddings of Schatten Norms with Applications to Data Streams

Authors: Yi Li and David P. Woodruff

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
Given an n×d matrix A, its Schatten-p norm, p >= 1, is defined as |A|_p = (sum_{i=1}^rank(A) sigma(i)^p）^{1/p} where sigma_i(A) is the i-th largest singular value of A. These norms have been studied in functional analysis in the context of non-commutative L_p-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embeddability, are still open. Specifically, given a set of matrices A_1, ... , A_poly(nd) in R^{n x d}, suppose we want to construct a linear map L such that L(A_i) in R^{n' x d'} for each i, where n' < n and d' < d, and further, |A_i|p <= |L(A_i)|_q <= D_{p,q}|A_i|_p for a given approximation factor D_{p,q} and real number q >= 1. Then how large do n' and d' need to be as a function of D_{p,q}? We nearly resolve this question for every p, q >= 1, for the case where L(A_i) can be expressed as R*A_i*S, where R and S are arbitrary matrices that are allowed to depend on A_1, ... ,A_t, that is, L(A_i) can be implemented by left and right matrix multiplication. Namely, for every p, q >= 1, we provide nearly matching upper and lower bounds on the size of n' and d' as a function of D_{p,q}. Importantly, our upper bounds are oblivious, meaning that R and S do not depend on the A_i, while our lower bounds hold even if R and S depend on the A_i. As an application of our upper bounds, we answer a recent open question of Blasiok et al. about space-approximation trade-offs for the Schatten 1-norm, showing in a data stream it is possible to estimate the Schatten-1 norm up to a factor of D >= 1 using O~(min(n, d)^2/D^4) space.
Cite as

Yi Li and David P. Woodruff. Embeddings of Schatten Norms with Applications to Data Streams. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{li_et_al:LIPIcs.ICALP.2017.60,
  author =	{Li, Yi and Woodruff, David P.},
  title =	{{Embeddings of Schatten Norms with Applications to Data Streams}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.60},
  URN =		{urn:nbn:de:0030-drops-73726},
  doi =		{10.4230/LIPIcs.ICALP.2017.60},
  annote =	{Keywords: data stream algorithms, embeddings, matrix norms, sketching}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.39
Tight Bounds for Sketching the Operator Norm, Schatten Norms, and Subspace Embeddings

Authors: Yi Li and David P. Woodruff

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

Abstract
We consider the following oblivious sketching problem: given epsilon in (0,1/3) and n >= d/epsilon^2, design a distribution D over R^{k * nd} and a function f: R^k * R^{nd} -> R}, so that for any n * d matrix A, Pr_{S sim D} [(1-epsilon) |A|_{op} <= f(S(A),S) <= (1+epsilon)|A|_{op}] >= 2/3, where |A|_{op} = sup_{x:|x|_2 = 1} |Ax|_2 is the operator norm of A and S(A) denotes S * A, interpreting A as a vector in R^{nd}. We show a tight lower bound of k = Omega(d^2/epsilon^2) for this problem. Previously, Nelson and Nguyen (ICALP, 2014) considered the problem of finding a distribution D over R^{k * n} such that for any n * d matrix A, Pr_{S sim D}[forall x, (1-epsilon)|Ax|_2 <= |SAx|_2 <= (1+epsilon)|Ax|_2] >= 2/3, which is called an oblivious subspace embedding (OSE). Our result considerably strengthens theirs, as it (1) applies only to estimating the operator norm, which can be estimated given any OSE, and (2) applies to distributions over general linear operators S which treat A as a vector and compute S(A), rather than the restricted class of linear operators corresponding to matrix multiplication. Our technique also implies the first tight bounds for approximating the Schatten p-norm for even integers p via general linear sketches, improving the previous lower bound from k = Omega(n^{2-6/p}) [Regev, 2014] to k = Omega(n^{2-4/p}). Importantly, for sketching the operator norm up to a factor of alpha, where alpha - 1 = \Omega(1), we obtain a tight k = Omega(n^2/alpha^4) bound, matching the upper bound of Andoni and Nguyen (SODA, 2013), and improving the previous k = Omega(n^2/\alpha^6) lower bound. Finally, we also obtain the first lower bounds for approximating Ky Fan norms.
Cite as

Yi Li and David P. Woodruff. Tight Bounds for Sketching the Operator Norm, Schatten Norms, and Subspace Embeddings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 39:1-39:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{li_et_al:LIPIcs.APPROX-RANDOM.2016.39,
  author =	{Li, Yi and Woodruff, David P.},
  title =	{{Tight Bounds for Sketching the Operator Norm, Schatten Norms, and Subspace Embeddings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{39:1--39:11},
  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.2016.39},
  URN =		{urn:nbn:de:0030-drops-66620},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.39},
  annote =	{Keywords: data streams, sketching, matrix norms, subspace embeddings}
}
Document
DOI: 10.4230/LIPIcs.CCC.2016.20
New Characterizations in Turnstile Streams with Applications

Authors: Yuqing Ai, Wei Hu, Yi Li, and David P. Woodruff

Published in: LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

Abstract
Recently, [Li, Nguyen, Woodruff, STOC 2014] showed any 1-pass constant probability streaming algorithm for computing a relation f on a vector x in {-m, -(m-1), ..., m}^n presented in the turnstile data stream model can be implemented by maintaining a linear sketch Ax mod q, where A is an r times n integer matrix and q = (q_1, ..., q_r) is a vector of positive integers. The space complexity of maintaining Ax mod q, not including the random bits used for sampling A and q, matches the space of the optimal algorithm. We give multiple strengthenings of this reduction, together with new applications. In particular, we show how to remove the following shortcomings of their reduction: 1. The Box Constraint. Their reduction applies only to algorithms that must be correct even if x_{infinity} = max_{i in [n]} |x_i| is allowed to be much larger than m at intermediate points in the stream, provided that x is in {-m, -(m-1), ..., m}^n at the end of the stream. We give a condition under which the optimal algorithm is a linear sketch even if it works only when promised that x is in {-m, -(m-1), ..., m}^n at all points in the stream. Using this, we show the first super-constant Omega(log m) bits lower bound for the problem of maintaining a counter up to an additive epsilon*m error in a turnstile stream, where epsilon is any constant in (0, 1/2). Previous lower bounds are based on communication complexity and are only for relative error approximation; interestingly, we do not know how to prove our result using communication complexity. More generally, we show the first super-constant Omega(log(m)) lower bound for additive approximation of l_p-norms; this bound is tight for p in [1, 2]. 2. Negative Coordinates. Their reduction allows x_i to be negative while processing the stream. We show an equivalence between 1-pass algorithms and linear sketches Ax mod q in dynamic graph streams, or more generally, the strict turnstile model, in which for all i in [n], x_i is nonnegative at all points in the stream. Combined with [Assadi, Khanna, Li, Yaroslavtsev, SODA 2016], this resolves the 1-pass space complexity of approximating the maximum matching in a dynamic graph stream, answering a question in that work. 3. 1-Pass Restriction. Their reduction only applies to 1-pass data stream algorithms in the turnstile model, while there exist algorithms for heavy hitters and for low rank approximation which provably do better with multiple passes. We extend the reduction to algorithms which make any number of passes, showing the optimal algorithm is to choose a new linear sketch at the beginning of each pass, based on the output of previous passes.
Cite as

Yuqing Ai, Wei Hu, Yi Li, and David P. Woodruff. New Characterizations in Turnstile Streams with Applications. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ai_et_al:LIPIcs.CCC.2016.20,
  author =	{Ai, Yuqing and Hu, Wei and Li, Yi and Woodruff, David P.},
  title =	{{New Characterizations in Turnstile Streams with Applications}},
  booktitle =	{31st Conference on Computational Complexity (CCC 2016)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-008-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{50},
  editor =	{Raz, Ran},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.20},
  URN =		{urn:nbn:de:0030-drops-58337},
  doi =		{10.4230/LIPIcs.CCC.2016.20},
  annote =	{Keywords: communication complexity, data streams, dynamic graph streams, norm estimation}
}

Li, Yingkai

Document
DOI: 10.4230/LIPIcs.ITCS.2023.9
Making Auctions Robust to Aftermarkets

Authors: Moshe Babaioff, Nicole Immorlica, Yingkai Li, and Brendan Lucier

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

Abstract
A prevalent assumption in auction theory is that the auctioneer has full control over the market and that the allocation she dictates is final. In practice, however, agents might be able to resell acquired items in an aftermarket. A prominent example is the market for carbon emission allowances. These allowances are commonly allocated by the government using uniform-price auctions, and firms can typically trade these allowances among themselves in an aftermarket that may not be fully under the auctioneer’s control. While the uniform-price auction is approximately efficient in isolation, we show that speculation and resale in aftermarkets might result in a significant welfare loss. Motivated by this issue, we consider three approaches, each ensuring high equilibrium welfare in the combined market. The first approach is to adopt smooth auctions such as discriminatory auctions. This approach is robust to correlated valuations and to participants acquiring information about others' types. However, discriminatory auctions have several downsides, notably that of charging bidders different prices for identical items, resulting in fairness concerns that make the format unpopular. Two other approaches we suggest are either using posted-pricing mechanisms, or using uniform-price auctions with anonymous reserves. We show that when using balanced prices, both these approaches ensure high equilibrium welfare in the combined market. The latter also inherits many of the benefits from uniform-price auctions such as price discovery, and can be introduced with a minor modification to auctions currently in use to sell carbon emission allowances.
Cite as

Moshe Babaioff, Nicole Immorlica, Yingkai Li, and Brendan Lucier. Making Auctions Robust to Aftermarkets. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{babaioff_et_al:LIPIcs.ITCS.2023.9,
  author =	{Babaioff, Moshe and Immorlica, Nicole and Li, Yingkai and Lucier, Brendan},
  title =	{{Making Auctions Robust to Aftermarkets}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{9:1--9:23},
  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.2023.9},
  URN =		{urn:nbn:de:0030-drops-175122},
  doi =		{10.4230/LIPIcs.ITCS.2023.9},
  annote =	{Keywords: carbon markets, aftermarkets, price of anarchy, multi-unit auctions, posted prices}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.52
Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence

Authors: Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins

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

Abstract
Online advertising via auctions increasingly dominates the marketing landscape. A typical advertiser may participate in thousands of auctions each day with bids tailored to a variety of signals about user demographics and intent. These auctions are strategically linked through a global budget constraint. To help address the difficulty of bidding, many major online platforms now provide automated budget management via a flexible approach called budget pacing: rather than bidding directly, an advertiser specifies a global budget target and a maximum willingness-to-pay for different types of advertising opportunities. The specified maximums are then scaled down (or "paced") by a multiplier so that the realized total spend matches the target budget. These automated bidders are now near-universally adopted across all mature advertising platforms, raising pressing questions about market outcomes that arise when advertisers use budget pacing simultaneously. In this paper we study the aggregate welfare and individual regret guarantees of dynamic pacing algorithms in repeated auctions with budgets. We show that when agents simultaneously use a natural form of gradient-based pacing, the liquid welfare obtained over the course of the dynamics is at least half the optimal liquid welfare obtainable by any allocation rule, matching the best possible bound for static auctions even in pure Nash equilibria [Aggarwal et al., WINE 2019; Babaioff et al., ITCS 2021]. In contrast to prior work, these results hold without requiring convergence of the dynamics, circumventing known computational obstacles of finding equilibria [Chen et al., EC 2021]. Our result is robust to the correlation structure among agents' valuations and holds for any core auction, a broad class that includes first-price, second-price, and GSP auctions. We complement the aggregate guarantees by showing that an agent using such pacing algorithms achieves an O(T^{3/4}) regret relative to the value obtained by the best fixed pacing multiplier in hindsight in stochastic bidding environments. Compared to past work, this result applies to more general auctions and extends to adversarial settings with respect to dynamic regret.
Cite as

Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins. Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, p. 52:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gaitonde_et_al:LIPIcs.ITCS.2023.52,
  author =	{Gaitonde, Jason and Li, Yingkai and Light, Bar and Lucier, Brendan and Slivkins, Aleksandrs},
  title =	{{Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{52:1--52:1},
  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.2023.52},
  URN =		{urn:nbn:de:0030-drops-175557},
  doi =		{10.4230/LIPIcs.ITCS.2023.52},
  annote =	{Keywords: repeated auctions with budgets, pacing, learning in auctions}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.108
Brief Announcement: Bayesian Auctions with Efficient Queries

Authors: Jing Chen, Bo Li, Yingkai Li, and Pinyan Lu

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

Abstract
Generating good revenue is one of the most important problems in Bayesian auction design, and many (approximately) optimal dominant-strategy incentive compatible (DSIC) Bayesian mechanisms have been constructed for various auction settings. However, most existing studies do not consider the complexity for the seller to carry out the mechanism. It is assumed that the seller knows "each single bit" of the distributions and is able to optimize perfectly based on the entire distributions. Unfortunately this is a strong assumption and may not hold in reality: for example, when the value distributions have exponentially large supports or do not have succinct representations. In this work we consider, for the first time, the query complexity of Bayesian mechanisms. We only allow the seller to have limited oracle accesses to the players' value distributions, via quantile queries and value queries. For a large class of auction settings, we prove logarithmic lower-bounds for the query complexity for any DSIC Bayesian mechanism to be of any constant approximation to the optimal revenue. For single-item auctions and multi-item auctions with unit-demand or additive valuation functions, we prove tight upper-bounds via efficient query schemes, without requiring the distributions to be regular or have monotone hazard rate. Thus, in those auction settings the seller needs to access much less than the full distributions in order to achieve approximately optimal revenue.
Cite as

Jing Chen, Bo Li, Yingkai Li, and Pinyan Lu. Brief Announcement: Bayesian Auctions with Efficient Queries. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 108:1-108:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2018.108,
  author =	{Chen, Jing and Li, Bo and Li, Yingkai and Lu, Pinyan},
  title =	{{Brief Announcement: Bayesian Auctions with Efficient Queries}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{108:1--108:4},
  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.2018.108},
  URN =		{urn:nbn:de:0030-drops-91124},
  doi =		{10.4230/LIPIcs.ICALP.2018.108},
  annote =	{Keywords: The complexity of Bayesian mechanisms, quantile queries, value queries}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.11
Efficient Approximations for the Online Dispersion Problem

Authors: Jing Chen, Bo Li, and Yingkai Li

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
The dispersion problem has been widely studied in computational geometry and facility location, and is closely related to the packing problem. The goal is to locate n points (e.g., facilities or persons) in a k-dimensional polytope, so that they are far away from each other and from the boundary of the polytope. In many real-world scenarios however, the points arrive and depart at different times, and decisions must be made without knowing future events. Therefore we study, for the first time in the literature, the online dispersion problem in Euclidean space. There are two natural objectives when time is involved: the all-time worst-case (ATWC) problem tries to maximize the minimum distance that ever appears at any time; and the cumulative distance (CD) problem tries to maximize the integral of the minimum distance throughout the whole time interval. Interestingly, the online problems are highly non-trivial even on a segment. For cumulative distance, this remains the case even when the problem is time-dependent but offline, with all the arriving and departure times given in advance. For the online ATWC problem on a segment, we construct a deterministic polynomial-time algorithm which is (2ln2+epsilon)-competitive, where epsilon>0 can be arbitrarily small and the algorithm's running time is polynomial in 1/epsilon. We show this algorithm is actually optimal. For the same problem in a square, we provide a 1.591-competitive algorithm and a 1.183 lower-bound. Furthermore, for arbitrary k-dimensional polytopes with k>=2, we provide a 2/(1-epsilon)-competitive algorithm and a 7/6 lower-bound. All our lower-bounds come from the structure of the online problems and hold even when computational complexity is not a concern. Interestingly, for the offline CD problem in arbitrary k-dimensional polytopes, we provide a polynomial-time black-box reduction to the online ATWC problem, and the resulting competitive ratio increases by a factor of at most 2. Our techniques also apply to online dispersion problems with different boundary conditions.
Cite as

Jing Chen, Bo Li, and Yingkai Li. Efficient Approximations for the Online Dispersion Problem. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2017.11,
  author =	{Chen, Jing and Li, Bo and Li, Yingkai},
  title =	{{Efficient Approximations for the Online Dispersion Problem}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.11},
  URN =		{urn:nbn:de:0030-drops-74002},
  doi =		{10.4230/LIPIcs.ICALP.2017.11},
  annote =	{Keywords: dispersion, online algorithms, geometric optimization, packing, competitive algorithms}
}

Li, Xinyi

Document
DOI: 10.4230/LIPIcs.ISAAC.2019.23
Approximating the Geometric Edit Distance

Authors: Kyle Fox and Xinyi Li

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a geometric space. Therefore, the geometric edit distance (GED) has been studied. In this paper, we describe the first strictly sublinear approximate near-linear time algorithm for computing the GED of two point sequences in constant dimensional Euclidean space. Specifically, we present a randomized O(n log^2n) time O(sqrt n)-approximation algorithm. Then, we generalize our result to give a randomized alpha-approximation algorithm for any alpha in [1, sqrt n], running in time O~(n^2/alpha^2). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability.
Cite as

Kyle Fox and Xinyi Li. Approximating the Geometric Edit Distance. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fox_et_al:LIPIcs.ISAAC.2019.23,
  author =	{Fox, Kyle and Li, Xinyi},
  title =	{{Approximating the Geometric Edit Distance}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.23},
  URN =		{urn:nbn:de:0030-drops-115195},
  doi =		{10.4230/LIPIcs.ISAAC.2019.23},
  annote =	{Keywords: Geometric edit distance, Approximation, Randomized algorithms}
}

Li, Liyi

Document
DOI: 10.4230/LIPIcs.ECOOP.2024.24
Qafny: A Quantum-Program Verifier

Authors: Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally requires significant effort. To address this challenge, we present Qafny, an automated proof system based on the program verifier Dafny and designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations modeled within a classical separation logic framework. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs and specifications into Dafny for automated verification purposes. We then illustrate the utility of Qafny’s automated capabilities in efficiently verifying important quantum algorithms, including quantum-walk algorithms, Grover’s algorithm, and Shor’s algorithm.
Cite as

Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu. Qafny: A Quantum-Program Verifier. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 24:1-24:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ECOOP.2024.24,
  author =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  title =	{{Qafny: A Quantum-Program Verifier}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{24:1--24:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.24},
  URN =		{urn:nbn:de:0030-drops-208735},
  doi =		{10.4230/LIPIcs.ECOOP.2024.24},
  annote =	{Keywords: Quantum Computing, Automated Verification, Separation Logic}
}
Document
Artifact
DOI: 10.4230/DARTS.10.2.12
Qafny: A Quantum-Program Verifier (Artifact)

Authors: Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu

Published in: DARTS, Volume 10, Issue 2, Special Issue of the 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
This artifact contains the Coq theory files for the Qafny proof system, including the formalism of the Qafny syntax, semantics, type system, and proof system, with the theorem proofs of type soundness, proof system soundness and completeness. It also contains a the compiled Dafny example programs generated from our Qafny-to-Dafny prototype compiler. These example programs serve as the validations of our Qafny-to-Dafny prototype compiler mechanism. The main work is introduced in the Qafny paper, which develops a separation logic style verification framework for quantum programs.
Cite as

Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu. Qafny: A Quantum-Program Verifier (Artifact). In Special Issue of the 38th European Conference on Object-Oriented Programming (ECOOP 2024). Dagstuhl Artifacts Series (DARTS), Volume 10, Issue 2, pp. 12:1-12:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{li_et_al:DARTS.10.2.12,
  author =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  title =	{{Qafny: A Quantum-Program Verifier (Artifact)}},
  pages =	{12:1--12:2},
  journal =	{Dagstuhl Artifacts Series},
  ISBN =	{978-3-95977-342-3},
  ISSN =	{2509-8195},
  year =	{2024},
  volume =	{10},
  number =	{2},
  editor =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.10.2.12},
  URN =		{urn:nbn:de:0030-drops-209104},
  doi =		{10.4230/DARTS.10.2.12},
  annote =	{Keywords: Quantum Computing, Automated Verification, Separation Logic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.21
Proving Quantum Programs Correct

Authors: Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Grover’s algorithm and quantum phase estimation, a key component of Shor’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain.
Cite as

Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks. Proving Quantum Programs Correct. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hietala_et_al:LIPIcs.ITP.2021.21,
  author =	{Hietala, Kesha and Rand, Robert and Hung, Shih-Han and Li, Liyi and Hicks, Michael},
  title =	{{Proving Quantum Programs Correct}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.21},
  URN =		{urn:nbn:de:0030-drops-139160},
  doi =		{10.4230/LIPIcs.ITP.2021.21},
  annote =	{Keywords: Formal Verification, Quantum Computing, Proof Engineering}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2020.7
K-LLVM: A Relatively Complete Semantics of LLVM IR

Authors: Liyi Li and Elsa L. Gunter

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract
LLVM [Lattner and Adve, 2004] is designed for the compile-time, link-time and run-time optimization of programs written in various programming languages. The language supported by LLVM targeted by modern compilers is LLVM IR [llvm.org, 2018]. In this paper we define K-LLVM, a reference semantics for LLVM IR. To the best of our knowledge, K-LLVM is the most complete formal LLVM IR semantics to date, including all LLVM IR instructions, intrinsic functions in the LLVM documentation and Standard-C library functions that are necessary to execute many LLVM IR programs. Additionally, K-LLVM formulates an abstract machine that executes all LLVM IR instructions. The machine allows to describe our formal semantics in terms of simulating a conceptual virtual machine that runs LLVM IR programs, including non-deterministic programs. Even though the K-LLVM memory model in this paper is assumed to be a sequentially consistent memory model and does not include all LLVM concurrency memory behaviors, the design of K-LLVM’s data layout allows the K-LLVM abstract machine to execute some LLVM IR programs that previous semantics did not cover, such as the full range of LLVM IR behaviors for the interaction among LLVM IR casting, pointer arithmetic, memory operations and some memory flags (e.g. readonly) of function headers. Additionally, the memory model is modularized in a manner that supports investigating other memory models. To validate K-LLVM, we have implemented it in 𝕂 [Roşu, 2016], which generated an interpreter for LLVM IR. Using this, we ran tests including 1,385 unit test programs and around 3,000 concrete LLVM IR programs, and K-LLVM passed all of them.
Cite as

Liyi Li and Elsa L. Gunter. K-LLVM: A Relatively Complete Semantics of LLVM IR. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 7:1-7:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{li_et_al:LIPIcs.ECOOP.2020.7,
  author =	{Li, Liyi and Gunter, Elsa L.},
  title =	{{K-LLVM: A Relatively Complete Semantics of LLVM IR}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{7:1--7:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.7},
  URN =		{urn:nbn:de:0030-drops-131649},
  doi =		{10.4230/LIPIcs.ECOOP.2020.7},
  annote =	{Keywords: LLVM, formal semantics, K framework, memory model, abstract machine}
}

Li, Yinan

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.110
Quantum Algorithms for Matrix Scaling and Matrix Balancing

Authors: Joran van Apeldoorn, Sander Gribling, Yinan Li, Harold Nieuwboer, Michael Walter, and Ronald de Wolf

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the power and limitations of quantum algorithms for these problems. We provide quantum implementations of two classical (in both senses of the word) methods: Sinkhorn’s algorithm for matrix scaling and Osborne’s algorithm for matrix balancing. Using amplitude estimation as our main tool, our quantum implementations both run in time Õ(√{mn}/ε⁴) for scaling or balancing an n × n matrix (given by an oracle) with m non-zero entries to within 𝓁₁-error ε. Their classical analogs use time Õ(m/ε²), and every classical algorithm for scaling or balancing with small constant ε requires Ω(m) queries to the entries of the input matrix. We thus achieve a polynomial speed-up in terms of n, at the expense of a worse polynomial dependence on the obtained 𝓁₁-error ε. Even for constant ε these problems are already non-trivial (and relevant in applications). Along the way, we extend the classical analysis of Sinkhorn’s and Osborne’s algorithm to allow for errors in the computation of marginals. We also adapt an improved analysis of Sinkhorn’s algorithm for entrywise-positive matrices to the 𝓁₁-setting, obtaining an Õ(n^{1.5}/ε³)-time quantum algorithm for ε-𝓁₁-scaling. We also prove a lower bound, showing our quantum algorithm for matrix scaling is essentially optimal for constant ε: every quantum algorithm for matrix scaling that achieves a constant 𝓁₁-error w.r.t. uniform marginals needs Ω(√{mn}) queries.
Cite as

Joran van Apeldoorn, Sander Gribling, Yinan Li, Harold Nieuwboer, Michael Walter, and Ronald de Wolf. Quantum Algorithms for Matrix Scaling and Matrix Balancing. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 110:1-110:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{vanapeldoorn_et_al:LIPIcs.ICALP.2021.110,
  author =	{van Apeldoorn, Joran and Gribling, Sander and Li, Yinan and Nieuwboer, Harold and Walter, Michael and de Wolf, Ronald},
  title =	{{Quantum Algorithms for Matrix Scaling and Matrix Balancing}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{110:1--110:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.110},
  URN =		{urn:nbn:de:0030-drops-141793},
  doi =		{10.4230/LIPIcs.ICALP.2021.110},
  annote =	{Keywords: Matrix scaling, matrix balancing, quantum algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.26
Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice

Authors: Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Motivated by testing isomorphism of p-groups, we study the alternating matrix space isometry problem (AltMatSpIso), which asks to decide whether two m-dimensional subspaces of n×n alternating (skew-symmetric if the field is not of characteristic 2) matrices are the same up to a change of basis. Over a finite field 𝔽_p with some prime p≠2, solving AltMatSpIso in time p^O(n+m) is equivalent to testing isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. The latter problem has long been considered a bottleneck case for the group isomorphism problem. Recently, Li and Qiao presented an average-case algorithm for AltMatSpIso in time p^O(n) when n and m are linearly related (FOCS '17). In this paper, we present an average-case algorithm for AltMatSpIso in time p^O(n+m). Besides removing the restriction on the relation between n and m, our algorithm is considerably simpler, and the average-case analysis is stronger. We then implement our algorithm, with suitable modifications, in Magma. Our experiments indicate that it improves significantly over default (brute-force) algorithms for this problem.
Cite as

Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson. Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brooksbank_et_al:LIPIcs.ESA.2020.26,
  author =	{Brooksbank, Peter A. and Li, Yinan and Qiao, Youming and Wilson, James B.},
  title =	{{Improved Algorithms for Alternating Matrix Space Isometry: From Theory to Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.26},
  URN =		{urn:nbn:de:0030-drops-128920},
  doi =		{10.4230/LIPIcs.ESA.2020.26},
  annote =	{Keywords: Alternating Matrix Spaces, Average-case Algorithm, p-groups of Class 2nd Exponent p, Magma}
}

Li, Yishuai

Document
DOI: 10.4230/LIPIcs.ITP.2021.32
Verifying an HTTP Key-Value Server with Interaction Trees and VST

Authors: Hengchu Zhang, Wolf Honoré, Nicolas Koh, Yao Li, Yishuai Li, Li-Yao Xia, Lennart Beringer, William Mansky, Benjamin Pierce, and Steve Zdancewic

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We present a networked key-value server, implemented in C and formally verified in Coq. The server interacts with clients using a subset of the HTTP/1.1 protocol and is specified and verified using interaction trees and the Verified Software Toolchain. The codebase includes a reusable and fully verified C string library that provides 17 standard POSIX string functions and 17 general purpose non-POSIX string functions. For the KVServer socket system calls, we establish a refinement relation between specifications at user-space level and at CertiKOS kernel-space level.
Cite as

Hengchu Zhang, Wolf Honoré, Nicolas Koh, Yao Li, Yishuai Li, Li-Yao Xia, Lennart Beringer, William Mansky, Benjamin Pierce, and Steve Zdancewic. Verifying an HTTP Key-Value Server with Interaction Trees and VST. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{zhang_et_al:LIPIcs.ITP.2021.32,
  author =	{Zhang, Hengchu and Honor\'{e}, Wolf and Koh, Nicolas and Li, Yao and Li, Yishuai and Xia, Li-Yao and Beringer, Lennart and Mansky, William and Pierce, Benjamin and Zdancewic, Steve},
  title =	{{Verifying an HTTP Key-Value Server with Interaction Trees and VST}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.32},
  URN =		{urn:nbn:de:0030-drops-139273},
  doi =		{10.4230/LIPIcs.ITP.2021.32},
  annote =	{Keywords: formal verification, Coq, HTTP, deep specification}
}
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