8 Search Results for "Simon, Hans Ulrich"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.50
On the PTAS Complexity of Multidimensional Knapsack

Authors: Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi

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

Abstract
We study the d-dimensional knapsack problem. We are given a set of items, each with a d-dimensional cost vector and a profit, along with a d-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A polynomial-time approximation scheme (PTAS) with running time n^{Θ(d/{ε})} has long been known for this problem, where {ε} is the error parameter and n is the encoding size. Despite decades of active research, the best running time of a PTAS has remained O(n^{⌈ d/{ε} ⌉ - d}). Unfortunately, existing lower bounds only cover the special case with two dimensions d = 2, and do not answer whether there is a n^{o(d/({ε)})}-time PTAS for larger values of d. In this work, we show that the running times of the best-known PTAS cannot be improved up to a polylogarithmic factor assuming the Exponential Time Hypothesis (ETH). Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions. Then, using a recent result of [Bafna Karthik and Minzer, STOC'25], we succeed in exhibiting tight trade-off between d and {ε} for all regimes of the parameters assuming d is sufficiently large. Informally, our result also shows that under ETH, for any function f there is no f(d/({ε)}) ⋅ n^{õ(d/({ε)})}-time (1-{ε})-approximation for d-dimensional knapsack, where n is the number of items and õ hides polylogarithmic factors in d/({ε)}.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi. On the PTAS Complexity of Multidimensional Knapsack. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{doronarad_et_al:LIPIcs.ITCS.2026.50,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Manurangsi, Pasin},
  title =	{{On the PTAS Complexity of Multidimensional Knapsack}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{50:1--50:22},
  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.2026.50},
  URN =		{urn:nbn:de:0030-drops-253377},
  doi =		{10.4230/LIPIcs.ITCS.2026.50},
  annote =	{Keywords: d-dimensional Knapsack, Multidimensional Knapsack, PTAS, CSP}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.35
Fooling Near-Maximal Decision Trees

Authors: William M. Hoza and Zelin Lv

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

Abstract
For any constant α > 0, we construct an explicit pseudorandom generator (PRG) that fools n-variate decision trees of size m with error ε and seed length (1 + α) ⋅ log₂ m + O(log(1/ε) + log log n). For context, one can achieve seed length (2 + o(1)) ⋅ log₂ m + O(log(1/ε) + log log n) using well-known constructions and analyses of small-bias distributions, but such a seed length is trivial when m ≥ 2^{n/2}. Our approach is to develop a new variant of the classic concept of almost k-wise independence, which might be of independent interest. We say that a distribution X over {0, 1}ⁿ is k-wise ε-probably uniform if every Boolean function f that depends on only k variables satisfies 𝔼[f(X)] ≥ (1 - ε) ⋅ 𝔼[f]. We show how to sample a k-wise ε-probably uniform distribution using a seed of length (1 + α) ⋅ k + O(log(1/ε) + log log n). Meanwhile, we also show how to construct a set H ⊆ 𝔽₂ⁿ such that every feasible system of k linear equations in n variables over 𝔽₂ has a solution in H. The cardinality of H and the time complexity of enumerating H are at most 2^{k + o(k) + polylog n}, whereas small-bias distributions would give a bound of 2^{2k + O(log(n/k))}. By combining our new constructions with work by Chen and Kabanets (TCS 2016), we obtain nontrivial PRGs and hitting sets for linear-size Boolean circuits. Specifically, we get an explicit PRG with seed length (1 - Ω(1)) ⋅ n that fools circuits of size 2.99 ⋅ n over the U₂ basis, and we get a hitting set with time complexity 2^{(1 - Ω(1)) ⋅ n} for circuits of size 2.49 ⋅ n over the B₂ basis.
Cite as

William M. Hoza and Zelin Lv. Fooling Near-Maximal Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.35,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{Fooling Near-Maximal Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{35:1--35:24},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-244019},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.35},
  annote =	{Keywords: almost k-wise independence, decision trees, pseudorandom generators}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.12
Online Knapsack Problems with Estimates

Authors: Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker

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

Abstract
Imagine you are a computer scientist who enjoys attending conferences or workshops within the year. Sadly, your travel budget is limited, so you must select a subset of events you can travel to. When you are aware of all possible events and their costs at the beginning of the year, you can select the subset of the possible events that maximizes your happiness and is within your budget. On the other hand, if you are blind about the options, you will likely have a hard time when trying to decide if you want to register somewhere or not, and will likely regret decisions you made in the future. These scenarios can be modeled by knapsack variants, either by an offline or an online problem. However, both scenarios are somewhat unrealistic: Usually, you will not know the exact costs of each workshop at the beginning of the year. The online version, however, is too pessimistic, as you might already know which options there are and how much they cost roughly. At some point, you have to decide whether to register for some workshop, but then you are aware of the conference fee and the flight and hotel prices. We model this problem within the setting of online knapsack problems with estimates: in the beginning, you receive a list of potential items with their estimated size as well as the accuracy of the estimates. Then, the items are revealed one by one in an online fashion with their actual size, and you need to decide whether to take one or not. In this article, we show a best-possible algorithm for each estimate accuracy δ (i.e., when each actual item size can deviate by ± δ from the announced size) for both the simple knapsack (also known as subset sum problem) and the simple knapsack with removability.
Cite as

Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker. Online Knapsack Problems with Estimates. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.12,
  author =	{Balab\'{a}n, Jakub and Gehnen, Matthias and Lotze, Henri and Seesemann, Finn and Stocker, Moritz},
  title =	{{Online Knapsack Problems with Estimates}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{12:1--12:19},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-241190},
  doi =		{10.4230/LIPIcs.MFCS.2025.12},
  annote =	{Keywords: Knapsack, Online Knapsack, Removability, Estimate, Prediction}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.11
When Alpha-Complexes Collapse onto Codimension-1 Submanifolds

Authors: Dominique Attali, Mattéo Clémot, Bianca B. Dornelas, and André Lieutier

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a finite set of points P sampling an unknown smooth surface ℳ ⊆ ℝ³, our goal is to triangulate ℳ based solely on P. Assuming ℳ is a smooth orientable submanifold of codimension 1 in ℝ^d, we introduce a simple algorithm, Naive Squash, which simplifies the α-complex of P by repeatedly applying a new type of collapse called vertical relative to ℳ. Naive Squash also has a practical version that does not require knowledge of ℳ. We establish conditions under which both the naive and practical Squash algorithms output a triangulation of ℳ. We provide a bound on the angle formed by triangles in the α-complex with ℳ, yielding sampling conditions on P that are competitive with existing literature for smooth surfaces embedded in ℝ³, while offering a more compartmentalized proof. As a by-product, we obtain that the restricted Delaunay complex of P triangulates ℳ when ℳ is a smooth surface in ℝ³ under weaker conditions than existing ones.
Cite as

Dominique Attali, Mattéo Clémot, Bianca B. Dornelas, and André Lieutier. When Alpha-Complexes Collapse onto Codimension-1 Submanifolds. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{attali_et_al:LIPIcs.SoCG.2025.11,
  author =	{Attali, Dominique and Cl\'{e}mot, Matt\'{e}o and Dornelas, Bianca B. and Lieutier, Andr\'{e}},
  title =	{{When Alpha-Complexes Collapse onto Codimension-1 Submanifolds}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.11},
  URN =		{urn:nbn:de:0030-drops-231630},
  doi =		{10.4230/LIPIcs.SoCG.2025.11},
  annote =	{Keywords: Submanifold reconstruction, triangulation, abstract simplicial complexes, collapses, convexity}
}
Document
DOI: 10.4230/OASIcs.FMBC.2025.10
Program Logics for Ledgers

Authors: Orestis Melkonian, Wouter Swierstra, and James Chapman

Published in: OASIcs, Volume 129, 6th International Workshop on Formal Methods for Blockchains (FMBC 2025)

Abstract
Distributed ledgers nowadays manage substantial monetary funds in the form of cryptocurrencies such as Bitcoin, Ethereum, and Cardano. For such ledgers to be safe, operations that add new entries must be cryptographically sound - but it is less clear how to reason effectively about such ever-growing linear data structures. This paper demonstrates how distributed ledgers may be viewed as computer programs, that, when executed, transfer funds between various parties. As a result, familiar program logics, such as Hoare logic, are applied in a novel setting. Borrowing ideas from concurrent separation logic, this enables modular reasoning principles over arbitrary fragments of any ledger. All of our results have been mechanised in the Agda proof assistant.
Cite as

Orestis Melkonian, Wouter Swierstra, and James Chapman. Program Logics for Ledgers. In 6th International Workshop on Formal Methods for Blockchains (FMBC 2025). Open Access Series in Informatics (OASIcs), Volume 129, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{melkonian_et_al:OASIcs.FMBC.2025.10,
  author =	{Melkonian, Orestis and Swierstra, Wouter and Chapman, James},
  title =	{{Program Logics for Ledgers}},
  booktitle =	{6th International Workshop on Formal Methods for Blockchains (FMBC 2025)},
  pages =	{10:1--10:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-371-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{129},
  editor =	{Marmsoler, Diego and Xu, Meng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2025.10},
  URN =		{urn:nbn:de:0030-drops-230370},
  doi =		{10.4230/OASIcs.FMBC.2025.10},
  annote =	{Keywords: blockchain, distributed ledgers, UTxO separation logic, program semantics, formal verification, Agda}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.185
Unlabeled Data Does Provably Help

Authors: Malte Darnstädt, Hans Ulrich Simon, and Balázs Szörényi

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
A fully supervised learner needs access to correctly labeled examples whereas a semi-supervised learner has access to examples part of which are labeled and part of which are not. The hope is that a large collection of unlabeled examples significantly reduces the need for labeled-ones. It is widely believed that this reduction of "label complexity" is marginal unless the hidden target concept and the domain distribution satisfy some "compatibility assumptions". There are some recent papers in support of this belief. In this paper, we revitalize the discussion by presenting a result that goes in the other direction. To this end, we consider the PAC-learning model in two settings: the (classical) fully supervised setting and the semi-supervised setting. We show that the "label-complexity gap"' between the semi-supervised and the fully supervised setting can become arbitrarily large for concept classes of infinite VC-dimension (or sequences of classes whose VC-dimensions are finite but become arbitrarily large). On the other hand, this gap is bounded by O(ln |C|) for each finite concept class C that contains the constant zero- and the constant one-function. A similar statement holds for all classes C of finite VC-dimension.
Cite as

Malte Darnstädt, Hans Ulrich Simon, and Balázs Szörényi. Unlabeled Data Does Provably Help. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 185-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{darnstadt_et_al:LIPIcs.STACS.2013.185,
  author =	{Darnst\"{a}dt, Malte and Simon, Hans Ulrich and Sz\"{o}r\'{e}nyi, Bal\'{a}zs},
  title =	{{Unlabeled Data Does Provably Help}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{185--196},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.185},
  URN =		{urn:nbn:de:0030-drops-39337},
  doi =		{10.4230/LIPIcs.STACS.2013.185},
  annote =	{Keywords: algorithmic learning, sample complexity, semi-supervised learning}
}
Document
DOI: 10.4230/DagSemRep.163
Theory and Practice of Machine Learning (Dagstuhl Seminar 9702)

Authors: Thomas G. Dietterich, Wolfgang Maass, Hans Ulrich Simon, and Robert S. Sutton

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Thomas G. Dietterich, Wolfgang Maass, Hans Ulrich Simon, and Robert S. Sutton. Theory and Practice of Machine Learning (Dagstuhl Seminar 9702). Dagstuhl Seminar Report 163, pp. 1-33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1997)

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@TechReport{dietterich_et_al:DagSemRep.163,
  author =	{Dietterich, Thomas G. and Maass, Wolfgang and Simon, Hans Ulrich and Sutton, Robert S.},
  title =	{{Theory and Practice of Machine Learning (Dagstuhl Seminar 9702)}},
  pages =	{1--33},
  ISSN =	{1619-0203},
  year =	{1997},
  type = 	{Dagstuhl Seminar Report},
  number =	{163},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.163},
  URN =		{urn:nbn:de:0030-drops-150503},
  doi =		{10.4230/DagSemRep.163},
}
Document
DOI: 10.4230/DagSemRep.91
Theory and Praxis of Machine Learning (Dagstuhl Seminar 9426)

Authors: Thomas Dietterich, Wolfgang Maass, Hans-Ulrich Simon, and Manfred Warmuth

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Thomas Dietterich, Wolfgang Maass, Hans-Ulrich Simon, and Manfred Warmuth. Theory and Praxis of Machine Learning (Dagstuhl Seminar 9426). Dagstuhl Seminar Report 91, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (1994)

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@TechReport{dietterich_et_al:DagSemRep.91,
  author =	{Dietterich, Thomas and Maass, Wolfgang and Simon, Hans-Ulrich and Warmuth, Manfred},
  title =	{{Theory and Praxis of Machine Learning (Dagstuhl Seminar 9426)}},
  pages =	{1--24},
  ISSN =	{1619-0203},
  year =	{1994},
  type = 	{Dagstuhl Seminar Report},
  number =	{91},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemRep.91},
  URN =		{urn:nbn:de:0030-drops-149796},
  doi =		{10.4230/DagSemRep.91},
}
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