16 Search Results for "Reichman, Daniel"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.102
Smoothed Analysis of Dynamic Graph Algorithms

Authors: Uri Meir and Ami Paz

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and Yu, FOCS 2023). As worst-case analysis (adversarial inputs) may lead to the necessity of high running times, a natural question arises: in which cases are high running times really necessary, and in which cases these inputs merely manifest unique pathological cases? Early attempts to tackle this question were made by Nikoletseas, Reif, Spirakis and Yung (ICALP 1995) and by Alberts and Henzinger (Algorithmica 1998), who considered models with very little adversarial control over the inputs, and showed fast algorithms exist for them. The question was then overlooked for decades, until Henzinger, Lincoln and Saha (SODA 2022) recently addressed uniformly random inputs, and presented algorithms and impossibility results for several subgraph counting problems. To tackle the above question more thoroughly, we employ smoothed analysis, a celebrated framework introduced by Spielman and Teng (J. ACM, 2004). An input is proposed by an adversary but then a noisy version of it is processed by the algorithm instead. This model of inputs is parameterized by the amount of adversarial control, and fully interpolates between worst-case inputs and a uniformly random input. Doing so, we extend impossibility results for some problems to the smoothed model with only a minor quantitative loss. That is, we show that partially-adversarial inputs suffice to impose high running times for certain problems. In contrast, we show that other problems become easy even with the slightest amount of noise. In addition, we study the interplay between the adversary and the noise, leading to three natural models of smoothed inputs, for which we show a hierarchy of increasing difficulty stretching between the average-case and the worst-case complexities.
Cite as

Uri Meir and Ami Paz. Smoothed Analysis of Dynamic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{meir_et_al:LIPIcs.ITCS.2026.102,
  author =	{Meir, Uri and Paz, Ami},
  title =	{{Smoothed Analysis of Dynamic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{102:1--102:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.102},
  URN =		{urn:nbn:de:0030-drops-253896},
  doi =		{10.4230/LIPIcs.ITCS.2026.102},
  annote =	{Keywords: Dynamic graph algorithms, Smoothed analysis, Shortest paths}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.30
Team Formation and Applications

Authors: Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph, using bounded size messages, where a certain fraction of the nodes may experience a generalized, strictly stronger, version of initial failures. The goal of a TF algorithm is to assemble tokens injected by the environment, in a distributed manner, into teams of size σ, where σ is a parameter of the problem. The usefulness of TF is demonstrated by using it to derive efficient algorithms for many distributed problems. Specifically, we show that various (one-shot as well as long-lived) distributed problems reduce to TF. This includes well-known (and extensively studied) distributed problems such as several versions of leader election and threshold detection. For example, we are the first to break the linear message complexity bound for asynchronous implicit leader election. We also improve the time complexity of message-optimal algorithms for asynchronous explicit leader election. Other distributed problems that reduce to TF are new ones, including matching players in online gaming platforms, a generalization of gathering, constructing a perfect matching in an induced subgraph of the complete graph, and more. To complement our positive contribution, we establish a tight lower bound on the message complexity of TF algorithms.
Cite as

Yuval Emek, Shay Kutten, Ido Rafael, and Gadi Taubenfeld. Team Formation and Applications. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 30:1-30:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{emek_et_al:LIPIcs.DISC.2025.30,
  author =	{Emek, Yuval and Kutten, Shay and Rafael, Ido and Taubenfeld, Gadi},
  title =	{{Team Formation and Applications}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{30:1--30:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.30},
  URN =		{urn:nbn:de:0030-drops-248474},
  doi =		{10.4230/LIPIcs.DISC.2025.30},
  annote =	{Keywords: asynchronous message-passing, complete communication graph, initial failures, leader election, matching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.73
Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians

Authors: François Le Gall

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary k-local Hamiltonian acting on n qubits. We first consider the setting where a good "guiding state" is available, which is the main setting where quantum algorithms are expected to achieve an exponential speedup over classical methods. We show that a constant approximation (i.e., an approximation with constant relative accuracy) of the ground state energy can be computed classically in poly (1/χ,n) time and poly(n) space, where χ denotes the overlap between the guiding state and the ground state (as in prior works in dequantization, we assume sample-and-query access to the guiding state). This gives a significant improvement over the recent classical algorithm by Gharibian and Le Gall (SICOMP 2023), and matches (up to a polynomial overhead) both the time and space complexities of quantum algorithms for constant approximation of the ground state energy. We also obtain classical algorithms for higher-precision approximation. For the setting where no guided state is given (i.e., the standard version of the local Hamiltonian problem), we obtain a classical algorithm computing a constant approximation of the ground state energy in 2^O(n) time and poly(n) space. To our knowledge, before this work it was unknown how to classically achieve these bounds simultaneously, even for constant approximation. We also discuss complexity-theoretic aspects of our results.
Cite as

François Le Gall. Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{legall:LIPIcs.ESA.2025.73,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{73:1--73:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.73},
  URN =		{urn:nbn:de:0030-drops-245419},
  doi =		{10.4230/LIPIcs.ESA.2025.73},
  annote =	{Keywords: approximation algorithms, quantum computing, dequantization}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.47
Time Lower Bounds for the Metropolis Process and Simulated Annealing

Authors: Zongchen Chen, Dan Mikulincer, Daniel Reichman, and Alexander S. Wein

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results regarding the quality of approximation obtained by MP and SA (with polynomially many iterations) for NP-hard optimization problems. We provide rigorous lower bounds for MP and SA with respect to the classical maximum independent set problem when the algorithms are initialized from the empty set. We establish the existence of a family of graphs for which both MP and SA fail to find approximate solutions in polynomial time. More specifically, we show that for any ε ∈ (0,1) there are n-vertex graphs for which the probability SA (when limited to polynomially many iterations) will approximate the optimal solution within ratio Ω(1/n^{1-ε}) is exponentially small. Our lower bounds extend to graphs of constant average degree d, illustrating the failure of MP to achieve an approximation ratio of Ω(log(d)/d) in polynomial time. In some cases, our lower bounds apply even when the temperature is chosen adaptively. Finally, we prove exponential-time lower bounds when the inputs to these algorithms are bipartite graphs, and even trees, which are known to admit polynomial-time algorithms for the independent set problem.
Cite as

Zongchen Chen, Dan Mikulincer, Daniel Reichman, and Alexander S. Wein. Time Lower Bounds for the Metropolis Process and Simulated Annealing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.47,
  author =	{Chen, Zongchen and Mikulincer, Dan and Reichman, Daniel and Wein, Alexander S.},
  title =	{{Time Lower Bounds for the Metropolis Process and Simulated Annealing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.47},
  URN =		{urn:nbn:de:0030-drops-244138},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.47},
  annote =	{Keywords: Metropolis Process, Simulated Annealing, Independent Set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.29
A Universal Uniform Approximation Theorem for Neural Networks

Authors: Olivier Bournez, Johanne Cohen, and Adrian Wurm

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We show the existence of a fixed recurrent network capable of approximating any computable function with arbitrary precision, provided that an encoding of the function is given in the initial input. While uniform approximation over a compact domain is a well-known property of neural networks, we go further by proving that our network ensures effective uniform approximation - simultaneously ensuring: - Uniform approximation in the sup-norm sense, guaranteeing precision across the compact domain {[0,1]^d}; - Uniformity in the sense of computability theory (also referred to as effectivity or universality), meaning the same network works for all computable functions. Our result is obtained constructively, using original arguments. Moreover, our construction bridges computation theory with neural network approximation, providing new insights into the fundamental connections between circuit complexity and function representation. Furthermore, this connection extends beyond computability to complexity theory. The obtained network is efficient: if a function is computable or approximable in polynomial time in the Turing machine model, then the network requires only a polynomial number of recurrences or iterations to achieve the same level of approximation, and conversely. Moreover, the recurrent network can be assumed to be very narrow, strengthening the link our results and existing models of very deep learning, where uniform approximation properties have already been established.
Cite as

Olivier Bournez, Johanne Cohen, and Adrian Wurm. A Universal Uniform Approximation Theorem for Neural Networks. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bournez_et_al:LIPIcs.MFCS.2025.29,
  author =	{Bournez, Olivier and Cohen, Johanne and Wurm, Adrian},
  title =	{{A Universal Uniform Approximation Theorem for Neural Networks}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-241365},
  doi =		{10.4230/LIPIcs.MFCS.2025.29},
  annote =	{Keywords: Models of computation, Complexity theory, Formal neural networks}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.33
Faster Construction of a Planar Distance Oracle with Õ(1) Query Time

Authors: Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We show how to preprocess a weighted undirected n-vertex planar graph in Õ(n^{4/3}) time, such that the distance between any pair of vertices can then be reported in Õ(1) time. This improves the previous Õ(n^{3/2}) preprocessing time [JACM'23]. Our main technical contribution is a near optimal construction of additively weighted Voronoi diagrams in undirected planar graphs. Namely, given a planar graph G and a face f, we show that one can preprocess G in Õ(n) time such that given any weight assignment to the vertices of f one can construct the additively weighted Voronoi diagram of f in near optimal Õ(|f|) time. This improves the Õ(√{n|f|}) construction time of [JACM'23].
Cite as

Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann. Faster Construction of a Planar Distance Oracle with Õ(1) Query Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boneh_et_al:LIPIcs.ICALP.2025.33,
  author =	{Boneh, Itai and Golan, Shay and Mozes, Shay and Prigan, Daniel and Weimann, Oren},
  title =	{{Faster Construction of a Planar Distance Oracle with \~{O}(1) Query Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.33},
  URN =		{urn:nbn:de:0030-drops-234106},
  doi =		{10.4230/LIPIcs.ICALP.2025.33},
  annote =	{Keywords: Distance Oracle, Planar Graph, Construction Time}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.5
Covers in Optimal Space

Authors: Itai Boneh and Shay Golan

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
A cover of a string S is a string C such that every index of S is contained in some occurrence of C. First introduced by Apostolico and Ehrenfeucht [TCS'93] over 30 years ago, covers have since received significant attention in the string algorithms community. In this work, we present a space-efficient algorithm for computing a compact representation of all covers of a given string. Our algorithm requires only O(log n) additional memory while accessing the input string of length n in a read-only manner. Moreover, it runs in O(n) time, matching the best-known time complexity for this problem while achieving an exponential improvement in space usage.
Cite as

Itai Boneh and Shay Golan. Covers in Optimal Space. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2025.5,
  author =	{Boneh, Itai and Golan, Shay},
  title =	{{Covers in Optimal Space}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.5},
  URN =		{urn:nbn:de:0030-drops-230993},
  doi =		{10.4230/LIPIcs.CPM.2025.5},
  annote =	{Keywords: Cover, Read-only random access, small space}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.42
Nearest Neighbor Complexity and Boolean Circuits

Authors: Mason DiCicco, Vladimir Podolskii, and Daniel Reichman

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A nearest neighbor representation of a Boolean function f is a set of vectors (anchors) labeled by 0 or 1 such that f(x) = 1 if and only if the closest anchor to x is labeled by 1. This model was introduced by Hajnal, Liu and Turán [2022], who studied bounds on the minimum number of anchors required to represent Boolean functions under different choices of anchors (real vs. Boolean vectors) as well as the analogous model of k-nearest neighbors representations. We initiate a systematic study of the representational power of nearest and k-nearest neighbors through Boolean circuit complexity. To this end, we establish a close connection between Boolean functions with polynomial nearest neighbor complexity and those that can be efficiently represented by classes based on linear inequalities - min-plus polynomial threshold functions - previously studied in relation to threshold circuits. This extends an observation of Hajnal et al. [2022]. Next, we further extend the connection between nearest neighbor representations and circuits to the k-nearest neighbors case. As an outcome of these connections we obtain exponential lower bounds on the k-nearest neighbors complexity of explicit n-variate functions, assuming k ≤ n^{1-ε}. Previously, no superlinear lower bound was known for any k > 1. At the same time, we show that proving superpolynomial lower bounds for the k-nearest neighbors complexity of an explicit function for arbitrary k would require a breakthrough in circuit complexity. In addition, we prove an exponential separation between the nearest neighbor and k-nearest neighbors complexity (for unrestricted k) of an explicit function. These results address questions raised by [Hajnal et al., 2022] of proving strong lower bounds for k-nearest neighbors and understanding the role of the parameter k. Finally, we devise new bounds on the nearest neighbor complexity for several families of Boolean functions.
Cite as

Mason DiCicco, Vladimir Podolskii, and Daniel Reichman. Nearest Neighbor Complexity and Boolean Circuits. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dicicco_et_al:LIPIcs.ITCS.2025.42,
  author =	{DiCicco, Mason and Podolskii, Vladimir and Reichman, Daniel},
  title =	{{Nearest Neighbor Complexity and Boolean Circuits}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{42:1--42:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.42},
  URN =		{urn:nbn:de:0030-drops-226704},
  doi =		{10.4230/LIPIcs.ITCS.2025.42},
  annote =	{Keywords: Complexity, Nearest Neighbors, Circuits}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.19
Synchronized CTL over One-Counter Automata

Authors: Shaull Almagor, Daniel Assa, and Udi Boker

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
We consider the model-checking problem of Synchronized Computation-Tree Logic (CTL+Sync) over One-Counter Automata (OCAs). CTL+Sync augments CTL with temporal operators that require several paths to satisfy properties in a synchronous manner, e.g., the property "all paths should eventually see p at the same time". The model-checking problem for CTL+Sync over finite-state Kripke structures was shown to be in 𝖯^{NP^NP}. OCAs are labelled transition systems equipped with a non-negative counter that can be zero-tested. Thus, they induce infinite-state systems whose computation trees are not regular. The model-checking problem for CTL over OCAs was shown to be PSPACE-complete. We show that the model-checking problem for CTL+Sync over OCAs is decidable. However, the upper bound we give is non-elementary. We therefore proceed to study the problem for a central fragment of CTL+Sync, extending CTL with operators that require all paths to satisfy properties in a synchronous manner, and show that it is in EXP^NEXP (and in particular in EXPSPACE), by exhibiting a certain "segmented periodicity" in the computation trees of OCAs.
Cite as

Shaull Almagor, Daniel Assa, and Udi Boker. Synchronized CTL over One-Counter Automata. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{almagor_et_al:LIPIcs.FSTTCS.2023.19,
  author =	{Almagor, Shaull and Assa, Daniel and Boker, Udi},
  title =	{{Synchronized CTL over One-Counter Automata}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{19:1--19:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.19},
  URN =		{urn:nbn:de:0030-drops-193921},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.19},
  annote =	{Keywords: CTL, Synchronization, One Counter Automata, Model Checking}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.67
Downward Self-Reducibility in TFNP

Authors: Prahladh Harsha, Daniel Mitropolsky, and Alon Rosen

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

Abstract
A problem is downward self-reducible if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that all downward self-reducible problems are in PSPACE. In this paper, we initiate the study of downward self-reducible search problems which are guaranteed to have a solution - that is, the downward self-reducible problems in TFNP. We show that most natural PLS-complete problems are downward self-reducible and any downward self-reducible problem in TFNP is contained in PLS. Furthermore, if the downward self-reducible problem is in TFUP (i.e. it has a unique solution), then it is actually contained in UEOPL, a subclass of CLS. This implies that if integer factoring is downward self-reducible then it is in fact in UEOPL, suggesting that no efficient factoring algorithm exists using the factorization of smaller numbers.
Cite as

Prahladh Harsha, Daniel Mitropolsky, and Alon Rosen. Downward Self-Reducibility in TFNP. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 67:1-67:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{harsha_et_al:LIPIcs.ITCS.2023.67,
  author =	{Harsha, Prahladh and Mitropolsky, Daniel and Rosen, Alon},
  title =	{{Downward Self-Reducibility in TFNP}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{67:1--67:17},
  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.2023.67},
  URN =		{urn:nbn:de:0030-drops-175700},
  doi =		{10.4230/LIPIcs.ITCS.2023.67},
  annote =	{Keywords: downward self-reducibility, TFNP, TFUP, factoring, PLS, CLS}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.7
Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks

Authors: Hermish Mehta and Daniel Reichman

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

Abstract
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all k-vertex subgraphs of an n-vertex graph. When k is not too large, we give nearly tight bounds for this local treewidth parameter; we also derive nearly tight bounds for the local treewidth of noisy trees, trees where every non-edge is added independently with small probability. We apply our upper bounds on the local treewidth to obtain fixed parameter tractable algorithms (on random graphs and noisy trees) for edge-removal problems centered around containing a contagious process evolving over a network. In these problems, our main parameter of study is k, the number of initially "infected" vertices in the network. For the random graph models we consider and a certain range of parameters the running time of our algorithms on n-vertex graphs is 2^o(k) poly(n), improving upon the 2^Ω(k) poly(n) performance of the best-known algorithms designed for worst-case instances of these edge deletion problems.
Cite as

Hermish Mehta and Daniel Reichman. Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mehta_et_al:LIPIcs.APPROX/RANDOM.2022.7,
  author =	{Mehta, Hermish and Reichman, Daniel},
  title =	{{Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.7},
  URN =		{urn:nbn:de:0030-drops-171299},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.7},
  annote =	{Keywords: Graph Algorithms, Random Graphs, Data Structures and Algorithms, Discrete Mathematics}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.22
Tight Hardness Results for Training Depth-2 ReLU Networks

Authors: Surbhi Goel, Adam Klivans, Pasin Manurangsi, and Daniel Reichman

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural network that minimizes the square loss with respect to a given training set. We prove that this problem is NP-hard already for a network with a single ReLU. We also prove NP-hardness for outputting a weighted sum of k ReLUs minimizing the squared error (for k > 1) even in the realizable setting (i.e., when the labels are consistent with an unknown depth-2 ReLU network). We are also able to obtain lower bounds on the running time in terms of the desired additive error ε. To obtain our lower bounds, we use the Gap Exponential Time Hypothesis (Gap-ETH) as well as a new hypothesis regarding the hardness of approximating the well known Densest κ-Subgraph problem in subexponential time (these hypotheses are used separately in proving different lower bounds). For example, we prove that under reasonable hardness assumptions, any proper learning algorithm for finding the best fitting ReLU must run in time exponential in 1/ε². Together with a previous work regarding improperly learning a ReLU [Surbhi Goel et al., 2017], this implies the first separation between proper and improper algorithms for learning a ReLU. We also study the problem of properly learning a depth-2 network of ReLUs with bounded weights giving new (worst-case) upper bounds on the running time needed to learn such networks both in the realizable and agnostic settings. Our upper bounds on the running time essentially matches our lower bounds in terms of the dependency on ε.
Cite as

Surbhi Goel, Adam Klivans, Pasin Manurangsi, and Daniel Reichman. Tight Hardness Results for Training Depth-2 ReLU Networks. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goel_et_al:LIPIcs.ITCS.2021.22,
  author =	{Goel, Surbhi and Klivans, Adam and Manurangsi, Pasin and Reichman, Daniel},
  title =	{{Tight Hardness Results for Training Depth-2 ReLU Networks}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.22},
  URN =		{urn:nbn:de:0030-drops-135611},
  doi =		{10.4230/LIPIcs.ITCS.2021.22},
  annote =	{Keywords: ReLU, Learning Algorithm, Running Time Lower Bound}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.56
String Matching: Communication, Circuits, and Learning

Authors: Alexander Golovnev, Mika Göös, Daniel Reichman, and Igor Shinkar

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
String matching is the problem of deciding whether a given n-bit string contains a given k-bit pattern. We study the complexity of this problem in three settings. - Communication complexity. For small k, we provide near-optimal upper and lower bounds on the communication complexity of string matching. For large k, our bounds leave open an exponential gap; we exhibit some evidence for the existence of a better protocol. - Circuit complexity. We present several upper and lower bounds on the size of circuits with threshold and DeMorgan gates solving the string matching problem. Similarly to the above, our bounds are near-optimal for small k. - Learning. We consider the problem of learning a hidden pattern of length at most k relative to the classifier that assigns 1 to every string that contains the pattern. We prove optimal bounds on the VC dimension and sample complexity of this problem.
Cite as

Alexander Golovnev, Mika Göös, Daniel Reichman, and Igor Shinkar. String Matching: Communication, Circuits, and Learning. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{golovnev_et_al:LIPIcs.APPROX-RANDOM.2019.56,
  author =	{Golovnev, Alexander and G\"{o}\"{o}s, Mika and Reichman, Daniel and Shinkar, Igor},
  title =	{{String Matching: Communication, Circuits, and Learning}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{56:1--56:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.56},
  URN =		{urn:nbn:de:0030-drops-112717},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.56},
  annote =	{Keywords: string matching, communication complexity, circuit complexity, PAC learning}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.9
Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Authors: Omri Ben-Eliezer, Simon Korman, and Daniel Reichman

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

Abstract
Analyzing multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms to understand local properties of the data. We focus on the natural problem of testing pattern freeness: given a large d-dimensional array A and a fixed d-dimensional pattern P over a finite alphabet Gamma, we say that A is P-free if it does not contain a copy of the forbidden pattern P as a consecutive subarray. The distance of A to P-freeness is the fraction of the entries of A that need to be modified to make it P-free. For any epsilon > 0 and any large enough pattern P over any alphabet - other than a very small set of exceptional patterns - we design a tolerant tester that distinguishes between the case that the distance is at least epsilon and the case that the distance is at most a_d epsilon, with query complexity and running time c_d epsilon^{-1}, where a_d < 1 and c_d depend only on the dimension d. These testers only need to access uniformly random blocks of samples from the input A. To analyze the testers we establish several combinatorial results, including the following d-dimensional modification lemma, which might be of independent interest: For any large enough d-dimensional pattern P over any alphabet (excluding a small set of exceptional patterns for the binary case), and any d-dimensional array A containing a copy of P, one can delete this copy by modifying one of its locations without creating new P-copies in A. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data.
Cite as

Omri Ben-Eliezer, Simon Korman, and Daniel Reichman. Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2017.9,
  author =	{Ben-Eliezer, Omri and Korman, Simon and Reichman, Daniel},
  title =	{{Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{9:1--9:14},
  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.2017.9},
  URN =		{urn:nbn:de:0030-drops-74427},
  doi =		{10.4230/LIPIcs.ICALP.2017.9},
  annote =	{Keywords: Property testing, Sublinear algorithms, Pattern matching}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.80
On Percolation and NP-Hardness

Authors: Huck Bennett, Daniel Reichman, and Igor Shinkar

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
The edge-percolation and vertex-percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational hardness of problems whose inputs are obtained by applying percolation to worst-case instances. Specifically, we show that a number of classical N P-hard graph problems remain essentially as hard on percolated instances as they are in the worst-case (assuming NP !subseteq BPP). We also prove hardness results for other NP-hard problems such as Constraint Satisfaction Problems, where random deletions are applied to clauses or variables. We focus on proving the hardness of the Maximum Independent Set problem and the Graph Coloring problem on percolated instances. To show this we establish the robustness of the corresponding parameters alpha(.) and Chi(.) to percolation, which may be of independent interest. Given a graph G, let G' be the graph obtained by randomly deleting edges of G. We show that if alpha(G) is small, then alpha(G') remains small with probability at least 0.99. Similarly, we show that if Chi(G) is large, then Chi(G') remains large with probability at least 0.99.
Cite as

Huck Bennett, Daniel Reichman, and Igor Shinkar. On Percolation and NP-Hardness. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bennett_et_al:LIPIcs.ICALP.2016.80,
  author =	{Bennett, Huck and Reichman, Daniel and Shinkar, Igor},
  title =	{{On Percolation and NP-Hardness}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{80:1--80:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.80},
  URN =		{urn:nbn:de:0030-drops-62056},
  doi =		{10.4230/LIPIcs.ICALP.2016.80},
  annote =	{Keywords: percolation, NP-hardness, random subgraphs, chromatic number}
}
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