6 Search Results for "Wagner, Tal"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.24
Learning-Augmented Maximum Independent Set

Authors: Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n^(1-δ) for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2+ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Õ((√Δ)/ε)-approximation in O(m) time where Δ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε²) total queries and Õ(m) runtime.
Cite as

Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang. Learning-Augmented Maximum Independent Set. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{braverman_et_al:LIPIcs.APPROX/RANDOM.2024.24,
  author =	{Braverman, Vladimir and Dharangutte, Prathamesh and Shah, Vihan and Wang, Chen},
  title =	{{Learning-Augmented Maximum Independent Set}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.24},
  URN =		{urn:nbn:de:0030-drops-210179},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.24},
  annote =	{Keywords: Learning-augmented algorithms, maximum independent set, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.24
Hierarchical Stochastic SAT and Quality Assessment of Logic Locking

Authors: Christoph Scholl, Tobias Seufert, and Fabian Siegwolf

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Motivated by the application of quality assessment of logic locking we introduce Hierarchical Stochastic SAT (HSSAT) which generalizes Stochastic SAT (SSAT). We look into the complexity of HSSAT and for solving HSSAT formulas we provide a prototype solver which computes exact evaluation results (i.e., without any approximation and without any imprecision caused by numerical rounding errors). Finally, we perform an intensive experimental evaluation of our HSSAT solver in the context of quality assessment of logic locking.
Cite as

Christoph Scholl, Tobias Seufert, and Fabian Siegwolf. Hierarchical Stochastic SAT and Quality Assessment of Logic Locking. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{scholl_et_al:LIPIcs.SAT.2024.24,
  author =	{Scholl, Christoph and Seufert, Tobias and Siegwolf, Fabian},
  title =	{{Hierarchical Stochastic SAT and Quality Assessment of Logic Locking}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.24},
  URN =		{urn:nbn:de:0030-drops-205462},
  doi =		{10.4230/LIPIcs.SAT.2024.24},
  annote =	{Keywords: Stochastic Boolean Satisfiability, Hierarchical Stochastic SAT, Binary Decision Diagrams, Decision Procedure}
}
Document
DOI: 10.4230/LIPIcs.ITC.2024.8
Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing

Authors: Dana Dachman-Soled, Julian Loss, and Adam O'Neill

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract
We investigate the relationship between the classical RSA and factoring problems when preprocessing is considered. In such a model, adversaries can use an unbounded amount of precomputation to produce an "advice" string to then use during the online phase, when a problem instance becomes known. Previous work (e.g., [Bernstein, Lange ASIACRYPT '13]) has shown that preprocessing attacks significantly improve the runtime of the best-known factoring algorithms. Due to these improvements, we ask whether the relationship between factoring and RSA fundamentally changes when preprocessing is allowed. Specifically, we investigate whether there is a superpolynomial gap between the runtime of the best attack on RSA with preprocessing and on factoring with preprocessing. Our main result rules this out with respect to algorithms that perform generic computation on the RSA instance x^e od N yet arbitrary computation on the modulus N, namely a careful adaptation of the well-known generic ring model of Aggarwal and Maurer (Eurocrypt 2009) to the preprocessing setting. In particular, in this setting we show the existence of a factoring algorithm with polynomially related parameters, for any setting of RSA parameters. Our main technical contribution is a set of new information-theoretic techniques that allow us to handle or eliminate cases in which the Aggarwal and Maurer result does not yield a factoring algorithm in the standard model with parameters that are polynomially related to those of the RSA algorithm. These techniques include two novel compression arguments, and a variant of the Fiat-Naor/Hellman tables construction that is tailored to the factoring setting.
Cite as

Dana Dachman-Soled, Julian Loss, and Adam O'Neill. Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dachmansoled_et_al:LIPIcs.ITC.2024.8,
  author =	{Dachman-Soled, Dana and Loss, Julian and O'Neill, Adam},
  title =	{{Breaking RSA Generically Is Equivalent to Factoring, with Preprocessing}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{8:1--8:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.8},
  URN =		{urn:nbn:de:0030-drops-205163},
  doi =		{10.4230/LIPIcs.ITC.2024.8},
  annote =	{Keywords: RSA, factoring, generic ring model, preprocessing}
}
Document
DOI: 10.4230/LIPIcs.ITC.2024.11
Fast Secure Computations on Shared Polynomials and Applications to Private Set Operations

Authors: Pascal Giorgi, Fabien Laguillaumie, Lucas Ottow, and Damien Vergnaud

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract
Secure multi-party computation aims to allow a set of players to compute a given function on their secret inputs without revealing any other information than the result of the computation. In this work, we focus on the design of secure multi-party protocols for shared polynomial operations. We consider the classical model where the adversary is honest-but-curious, and where the coefficients (or any secret values) are either encrypted using an additively homomorphic encryption scheme or shared using a threshold linear secret-sharing scheme. Our protocols terminate after a constant number of rounds and minimize the number of secure multiplications. In their seminal article at PKC 2006, Mohassel and Franklin proposed constant-rounds protocols for the main operations on (shared) polynomials. In this work, we improve the fan-in multiplication of nonzero polynomials, the multi-point polynomial evaluation and the polynomial interpolation (on secret points) to reach a quasi-linear complexity (instead of quadratic in Mohassel and Franklin’s work) in the degree of shared input/output polynomials. Computing with shared polynomials is a core component of several multi-party protocols for privacy-preserving operations on private sets, like the private disjointness test or the private set intersection. Using our new protocols, we are able to improve the complexity of such protocols and to design the first variants which always return a correct result.
Cite as

Pascal Giorgi, Fabien Laguillaumie, Lucas Ottow, and Damien Vergnaud. Fast Secure Computations on Shared Polynomials and Applications to Private Set Operations. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{giorgi_et_al:LIPIcs.ITC.2024.11,
  author =	{Giorgi, Pascal and Laguillaumie, Fabien and Ottow, Lucas and Vergnaud, Damien},
  title =	{{Fast Secure Computations on Shared Polynomials and Applications to Private Set Operations}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.11},
  URN =		{urn:nbn:de:0030-drops-205194},
  doi =		{10.4230/LIPIcs.ITC.2024.11},
  annote =	{Keywords: Multi-party computation, polynomial operations, privacy-preserving set operations}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.35
Finer-Grained Hardness of Kernel Density Estimation

Authors: Josh Alman and Yunfeng Guan

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
In batch Kernel Density Estimation (KDE) for a kernel function f : ℝ^m × ℝ^m → ℝ, we are given as input 2n points x^{(1)}, …, x^{(n)}, y^{(1)}, …, y^{(n)} ∈ ℝ^m in dimension m, as well as a vector v ∈ ℝⁿ. These inputs implicitly define the n × n kernel matrix K given by K[i,j] = f(x^{(i)}, y^{(j)}). The goal is to compute a vector v ∈ ℝⁿ which approximates K w, i.e., with || Kw - v||_∞ < ε ||w||₁. For illustrative purposes, consider the Gaussian kernel f(x,y) : = e^{-||x-y||₂²}. The classic approach to this problem is the famous Fast Multipole Method (FMM), which runs in time n ⋅ O(log^m(ε^{-1})) and is particularly effective in low dimensions because of its exponential dependence on m. Recently, as the higher-dimensional case m ≥ Ω(log n) has seen more applications in machine learning and statistics, new algorithms have focused on this setting: an algorithm using discrepancy theory, which runs in time O(n / ε), and an algorithm based on the polynomial method, which achieves inverse polynomial accuracy in almost linear time when the input points have bounded square diameter B < o(log n). A recent line of work has proved fine-grained lower bounds, with the goal of showing that the "curse of dimensionality" arising in FMM is necessary assuming the Strong Exponential Time Hypothesis (SETH). Backurs et al. [NeurIPS 2017] first showed the hardness of a variety of Empirical Risk Minimization problems including KDE for Gaussian-like kernels in the case with high dimension m = Ω(log n) and large scale B = Ω(log n). Alman et al. [FOCS 2020] later developed new reductions in roughly this same parameter regime, leading to lower bounds for more general kernels, but only for very small error ε < 2^{- log^{Ω(1)} (n)}. In this paper, we refine the approach of Alman et al. to show new lower bounds in all parameter regimes, closing gaps between the known algorithms and lower bounds. For example: - In the setting where m = Clog n and B = o(log n), we prove Gaussian KDE requires n^{2-o(1)} time to achieve additive error ε < Ω(m/B)^{-m}, matching the performance of the polynomial method up to low-order terms. - In the low dimensional setting m = o(log n), we show that Gaussian KDE requires n^{2-o(1)} time to achieve ε such that log log (ε^{-1}) > ̃ Ω ((log n)/m), matching the error bound achievable by FMM up to low-order terms. To our knowledge, no nontrivial lower bound was previously known in this regime. Our approach also generalizes to any parameter regime and any kernel. For example, we achieve similar fine-grained hardness results for any kernel with slowly-decaying Taylor coefficients such as the Cauchy kernel. Our new lower bounds make use of an intricate analysis of the "counting matrix", a special case of the kernel matrix focused on carefully-chosen evaluation points. As a key technical lemma, we give a novel approach to bounding the entries of its inverse by using Schur polynomials from algebraic combinatorics.
Cite as

Josh Alman and Yunfeng Guan. Finer-Grained Hardness of Kernel Density Estimation. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 35:1-35:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alman_et_al:LIPIcs.CCC.2024.35,
  author =	{Alman, Josh and Guan, Yunfeng},
  title =	{{Finer-Grained Hardness of Kernel Density Estimation}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{35:1--35:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.35},
  URN =		{urn:nbn:de:0030-drops-204311},
  doi =		{10.4230/LIPIcs.CCC.2024.35},
  annote =	{Keywords: Kernel Density Estimation, Fine-Grained Complexity, Schur Polynomials}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.738
Towards Resistance Sparsifiers

Authors: Michael Dinitz, Robert Krauthgamer, and Tal Wagner

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

Abstract
We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular expander admits a (1+epsilon)-resistance sparsifier of size ~O(n/epsilon), and conjecture this bound holds for all graphs on n nodes. In comparison, spectral sparsification is a strictly stronger notion and requires Omega(n/epsilon^2) edges even on the complete graph. Our approach leads to the following structural question on graphs: Does every dense regular expander contain a sparse regular expander as a subgraph? Our main technical contribution, which may of independent interest, is a positive answer to this question in a certain setting of parameters. Combining this with a recent result of von Luxburg, Radl, and Hein (JMLR, 2014) leads to the aforementioned resistance sparsifiers.
Cite as

Michael Dinitz, Robert Krauthgamer, and Tal Wagner. Towards Resistance Sparsifiers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 738-755, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{dinitz_et_al:LIPIcs.APPROX-RANDOM.2015.738,
  author =	{Dinitz, Michael and Krauthgamer, Robert and Wagner, Tal},
  title =	{{Towards Resistance Sparsifiers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{738--755},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.738},
  URN =		{urn:nbn:de:0030-drops-53334},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.738},
  annote =	{Keywords: edge sparsification, spectral sparsifier, graph expansion, effective resistance, commute time}
}
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