36 Search Results for "Li, Yi"


Document
RANDOM
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
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
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}
}
Document
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
Invited Talk
Worst-Case Optimal Join Algorithms (Invited Talk)

Authors: Ke Yi

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)


Abstract
Join is the most important operator in relational databases, and remains the most expensive one despite years of research and engineering efforts. Following the ground-breaking work of Atserias, Grohe, and Marx in 2008, worst-case optimal join algorithms have been discovered, which has led to not only a series of beautiful theoretical results, but also new database systems based on drastically different query evaluation techniques. In this talk, I will present an overview of this topic, including algorithms in various computation models (sequential and parallel), variants of the problem (full, Boolean, and counting), and approximate solutions.

Cite as

Ke Yi. Worst-Case Optimal Join Algorithms (Invited Talk). In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, p. 2:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{yi:LIPIcs.ISAAC.2020.2,
  author =	{Yi, Ke},
  title =	{{Worst-Case Optimal Join Algorithms}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.2},
  URN =		{urn:nbn:de:0030-drops-133462},
  doi =		{10.4230/LIPIcs.ISAAC.2020.2},
  annote =	{Keywords: query evaluation}
}
Document
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}
}
Document
APPROX
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
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
Streaming Complexity of Spanning Tree Computation

Authors: Yi-Jun Chang, Martín Farach-Colton, Tsan-Sheng Hsu, and Meng-Tsung Tsai

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an n-node input graph to be read sequentially in p passes using Õ(n) space. If the list of edges includes deletions, then the model is called the turnstile model; otherwise it is called the insertion-only model. In both models, some graph problems, such as spanning trees, k-connectivity, densest subgraph, degeneracy, cut-sparsifier, and (Δ+1)-coloring, can be exactly solved or (1+ε)-approximated in a single pass; while other graph problems, such as triangle detection and unweighted all-pairs shortest paths, are known to require Ω̃(n) passes to compute. For many fundamental graph problems, the tractability in these models is open. In this paper, we study the tractability of computing some standard spanning trees, including BFS, DFS, and maximum-leaf spanning trees. Our results, in both the insertion-only and the turnstile models, are as follows. - Maximum-Leaf Spanning Trees: This problem is known to be APX-complete with inapproximability constant ρ ∈ [245/244, 2). By constructing an ε-MLST sparsifier, we show that for every constant ε > 0, MLST can be approximated in a single pass to within a factor of 1+ε w.h.p. (albeit in super-polynomial time for ε ≤ ρ-1 assuming P ≠ NP) and can be approximated in polynomial time in a single pass to within a factor of ρ_n+ε w.h.p., where ρ_n is the supremum constant that MLST cannot be approximated to within using polynomial time and Õ(n) space. In the insertion-only model, these algorithms can be deterministic. - BFS Trees: It is known that BFS trees require ω(1) passes to compute, but the naïve approach needs O(n) passes. We devise a new randomized algorithm that reduces the pass complexity to O(√n), and it offers a smooth tradeoff between pass complexity and space usage. This gives a polynomial separation between single-source and all-pairs shortest paths for unweighted graphs. - DFS Trees: It is unknown whether DFS trees require more than one pass. The current best algorithm by Khan and Mehta [STACS 2019] takes Õ(h) passes, where h is the height of computed DFS trees. Note that h can be as large as Ω(m/n) for n-node m-edge graphs. Our contribution is twofold. First, we provide a simple alternative proof of this result, via a new connection to sparse certificates for k-node-connectivity. Second, we present a randomized algorithm that reduces the pass complexity to O(√n), and it also offers a smooth tradeoff between pass complexity and space usage.

Cite as

Yi-Jun Chang, Martín Farach-Colton, Tsan-Sheng Hsu, and Meng-Tsung Tsai. Streaming Complexity of Spanning Tree Computation. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 34:1-34:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{chang_et_al:LIPIcs.STACS.2020.34,
  author =	{Chang, Yi-Jun and Farach-Colton, Mart{\'\i}n and Hsu, Tsan-Sheng and Tsai, Meng-Tsung},
  title =	{{Streaming Complexity of Spanning Tree Computation}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{34:1--34:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.34},
  URN =		{urn:nbn:de:0030-drops-118951},
  doi =		{10.4230/LIPIcs.STACS.2020.34},
  annote =	{Keywords: Max-Leaf Spanning Trees, BFS Trees, DFS Trees}
}
Document
Invited Paper
Matching mu-Logic: Foundation of K Framework (Invited Paper)

Authors: Xiaohong Chen and Grigore Roşu

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
K framework is an effort in realizing the ideal language framework where programming languages must have formal semantics and all languages tools are automatically generated from the formal semantics in a correct-by-construction manner at no additional costs. In this extended abstract, we present matching mu-logic as the foundation of K and discuss some of its applications in defining constructors, transition systems, modal mu-logic and temporal logic variants, and reachability logic.

Cite as

Xiaohong Chen and Grigore Roşu. Matching mu-Logic: Foundation of K Framework (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chen_et_al:LIPIcs.CALCO.2019.1,
  author =	{Chen, Xiaohong and Ro\c{s}u, Grigore},
  title =	{{Matching mu-Logic: Foundation of K Framework}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{1:1--1:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.1},
  URN =		{urn:nbn:de:0030-drops-114296},
  doi =		{10.4230/LIPIcs.CALCO.2019.1},
  annote =	{Keywords: Matching mu-logic, Program verification, Reachability logic}
}
Document
Emerging Hardware Techniques and EDA Methodologies for Neuromorphic Computing (Dagstuhl Seminar 19152)

Authors: Krishnendu Chakrabarty, Tsung-Yi Ho, Hai Li, and Ulf Schlichtmann

Published in: Dagstuhl Reports, Volume 9, Issue 4 (2019)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 19152 "Emerging Hardware Techniques and EDA Methodologies for Neuromorphic Computing," which was held during April 7–10, 2019 in Schloss Dagstuhl - Leibniz Center for Informatics. Though interdisciplinary considerations of issues from computer science in the domain of machine learning and large scale computing have already successfully been covered in a series of Dagstuhl seminars, this was the first time that Neuromorphic Computing was brought out as the focus. During the seminar, many of the participants presented their current research on the traditional and emerging hardware techniques, design methodologies, electronic design automation techniques, and application of neuromorphic computing, including ongoing work and open problems. This report documents the abstracts or extended abstracts of the talks presented during the seminar, as well as summaries of the discussion sessions.

Cite as

Krishnendu Chakrabarty, Tsung-Yi Ho, Hai Li, and Ulf Schlichtmann. Emerging Hardware Techniques and EDA Methodologies for Neuromorphic Computing (Dagstuhl Seminar 19152). In Dagstuhl Reports, Volume 9, Issue 4, pp. 43-58, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@Article{chakrabarty_et_al:DagRep.9.4.43,
  author =	{Chakrabarty, Krishnendu and Ho, Tsung-Yi and Li, Hai and Schlichtmann, Ulf},
  title =	{{Emerging Hardware Techniques and EDA Methodologies for Neuromorphic Computing (Dagstuhl Seminar 19152)}},
  pages =	{43--58},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{9},
  number =	{4},
  editor =	{Chakrabarty, Krishnendu and Ho, Tsung-Yi and Li, Hai and Schlichtmann, Ulf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.4.43},
  URN =		{urn:nbn:de:0030-drops-113034},
  doi =		{10.4230/DagRep.9.4.43},
  annote =	{Keywords: Neuromorphic computing; nanotechnology; hardware design; electronic design automation; reliability and robustness}
}
Document
Topological Data Analysis Reveals Principles of Chromosome Structure in Cellular Differentiation

Authors: Natalie Sauerwald, Yihang Shen, and Carl Kingsford

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)


Abstract
Topological data analysis (TDA) is a mathematically well-founded set of methods to derive robust information about the structure and topology of data. It has been applied successfully in several biological contexts. Derived primarily from algebraic topology, TDA rigorously identifies persistent features in complex data, making it well-suited to better understand the key features of three-dimensional chromosome structure. Chromosome structure has a significant influence in many diverse genomic processes and has recently been shown to relate to cellular differentiation. While there exist many methods to study specific substructures of chromosomes, we are still missing a global view of all geometric features of chromosomes. By applying TDA to the study of chromosome structure through differentiation across three cell lines, we provide insight into principles of chromosome folding and looping. We identify persistent connected components and one-dimensional topological features of chromosomes and characterize them across cell types and stages of differentiation. Availability: Scripts to reproduce the results from this study can be found at https://github.com/Kingsford-Group/hictda

Cite as

Natalie Sauerwald, Yihang Shen, and Carl Kingsford. Topological Data Analysis Reveals Principles of Chromosome Structure in Cellular Differentiation. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{sauerwald_et_al:LIPIcs.WABI.2019.23,
  author =	{Sauerwald, Natalie and Shen, Yihang and Kingsford, Carl},
  title =	{{Topological Data Analysis Reveals Principles of Chromosome Structure in Cellular Differentiation}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.23},
  URN =		{urn:nbn:de:0030-drops-110537},
  doi =		{10.4230/LIPIcs.WABI.2019.23},
  annote =	{Keywords: topological data analysis, chromosome structure, Hi-C, topologically associating domains}
}
Document
Alignment- and Reference-Free Phylogenomics with Colored de Bruijn Graphs

Authors: Roland Wittler

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)


Abstract
We present a new whole-genome based approach to infer large-scale phylogenies that is alignment- and reference-free. In contrast to other methods, it does not rely on pairwise comparisons to determine distances to infer edges in a tree. Instead, a colored de Bruijn graph is constructed, and information on common subsequences is extracted to infer phylogenetic splits. Application to different datasets confirms robustness of the approach. A comparison to other state-of-the-art whole-genome based methods indicates comparable or higher accuracy and efficiency.

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Roland Wittler. Alignment- and Reference-Free Phylogenomics with Colored de Bruijn Graphs. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{wittler:LIPIcs.WABI.2019.2,
  author =	{Wittler, Roland},
  title =	{{Alignment- and Reference-Free Phylogenomics with Colored de Bruijn Graphs}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.2},
  URN =		{urn:nbn:de:0030-drops-110325},
  doi =		{10.4230/LIPIcs.WABI.2019.2},
  annote =	{Keywords: Phylogenomics, phylogenetics, phylogenetic splits, colored de Bruijn graphs}
}
Document
Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs

Authors: Christian Konrad and Viktor Zamaraev

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We give deterministic distributed (1+epsilon)-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in O( (1 / epsilon) log n) rounds, and our independent set algorithm has a runtime of O( (1/epsilon) log(1/epsilon)log^* n) rounds. For coloring, existing lower bounds imply that the dependencies on 1/epsilon and log n are best possible. For independent set, we prove that Omega(1/epsilon) rounds are necessary. Both our algorithms make use of the tree decomposition of the input chordal graph. They iteratively peel off interval subgraphs, which are identified via the tree decomposition of the input graph, thereby partitioning the vertex set into O(log n) layers. For coloring, each interval graph is colored independently, which results in various coloring conflicts between the layers. These conflicts are then resolved in a separate phase, using the particular structure of our partitioning. For independent set, only the first O(log (1/epsilon)) layers are required as they already contain a large enough independent set. We develop a (1+epsilon)-approximation maximum independent set algorithm for interval graphs, which we then apply to those layers. This work raises the question as to how useful tree decompositions are for distributed computing.

Cite as

Christian Konrad and Viktor Zamaraev. Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{konrad_et_al:LIPIcs.MFCS.2019.21,
  author =	{Konrad, Christian and Zamaraev, Viktor},
  title =	{{Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.21},
  URN =		{urn:nbn:de:0030-drops-109651},
  doi =		{10.4230/LIPIcs.MFCS.2019.21},
  annote =	{Keywords: local model, approximation algorithms, minimum vertex coloring, maximum independent set, chordal graphs}
}
Document
RLE Edit Distance in Near Optimal Time

Authors: Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993.

Cite as

Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. RLE Edit Distance in Near Optimal Time. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{clifford_et_al:LIPIcs.MFCS.2019.66,
  author =	{Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{RLE Edit Distance in Near Optimal Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.66},
  URN =		{urn:nbn:de:0030-drops-110109},
  doi =		{10.4230/LIPIcs.MFCS.2019.66},
  annote =	{Keywords: String algorithms, Compression, Pattern matching, Run-length encoding}
}
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