12 Search Results for "Hay, David"

Document
DOI: 10.4230/OASIcs.ICPEC.2025.3
On the Use of Concept Maps to Improve Student Skills in an Introductory Object-Oriented Analysis and Design Course

Authors: José F. Vélez, A. Belén Moreno, Victoria Ruiz-Parrado, and Ángel Sánchez

Published in: OASIcs, Volume 133, 6th International Computer Programming Education Conference (ICPEC 2025)

Abstract
This paper presents an ongoing work on the application of concept maps to teaching an introductory Object-Oriented Analysis and Design course for Computer Science students. There exist previous works that introduce the concept map model in these object-oriented courses. However, these works do not usually go deeply enough into the transition from concept maps to static class diagrams. Although concept maps present some clear advantages when defining the abstractions present in object-oriented software modeling, some drawbacks may also appear if the transformation from these maps to class diagrams when the task is carried out through simplistic rules. In this paper we propose an approach, which is illustrated through a use case, to transition from a concept map to a static class diagram in a more realistic way.
Cite as

José F. Vélez, A. Belén Moreno, Victoria Ruiz-Parrado, and Ángel Sánchez. On the Use of Concept Maps to Improve Student Skills in an Introductory Object-Oriented Analysis and Design Course. In 6th International Computer Programming Education Conference (ICPEC 2025). Open Access Series in Informatics (OASIcs), Volume 133, pp. 3:1-3:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{velez_et_al:OASIcs.ICPEC.2025.3,
  author =	{V\'{e}lez, Jos\'{e} F. and Moreno, A. Bel\'{e}n and Ruiz-Parrado, Victoria and S\'{a}nchez, \'{A}ngel},
  title =	{{On the Use of Concept Maps to Improve Student Skills in an Introductory Object-Oriented Analysis and Design Course}},
  booktitle =	{6th International Computer Programming Education Conference (ICPEC 2025)},
  pages =	{3:1--3:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-393-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{133},
  editor =	{Queir\'{o}s, Ricardo and Pinto, M\'{a}rio and Portela, Filipe and Sim\~{o}es, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICPEC.2025.3},
  URN =		{urn:nbn:de:0030-drops-240337},
  doi =		{10.4230/OASIcs.ICPEC.2025.3},
  annote =	{Keywords: Object-Oriented Programming, Concept Map, Abstraction, Unified Modeling Language (UML), Static Class Diagram}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.6
Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes

Authors: Ricardo Rivera Cardoso, Alex Meiburg, and Daniel Nagaj

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Previously, all known variants of the Quantum Satisfiability (QSAT) problem - consisting of determining whether a k-local (k-body) Hamiltonian is frustration-free - could be classified as being either in 𝖯; or complete for NP, MA, or QMA₁. Here, we present new qubit variants of this problem that are complete for BQP₁, coRP, QCMA, PI(coRP,NP), PI(BQP₁,NP), PI(BQP₁,MA), SoPU(coRP,NP), SoPU(BQP₁,NP), and SoPU(BQP₁,MA). Our result implies that a complete classification of quantum constraint satisfaction problems (QCSPs), analogous to Schaefer’s dichotomy theorem for classical CSPs, must either include these 13 classes, or otherwise show that some are equal. Additionally, our result showcases two new types of QSAT problems that can be decided efficiently, as well as the first nontrivial BQP₁-complete problem. We first construct QSAT problems on qudits that are complete for BQP₁, coRP, and QCMA. These are made by restricting the finite set of Hamiltonians to consist of elements similar to H_{init}, H_{prop}, and H_{out}, seen in the circuit-to-Hamiltonian transformation. Usually, these are used to demonstrate hardness of QSAT and Local Hamiltonian problems, and so our proofs of hardness are simple. The difficulty lies in ensuring that all Hamiltonians generated with these three elements can be decided in their respective classes. For this, we build our Hamiltonian terms with high-dimensional data and clock qudits, ternary logic, and either monogamy of entanglement or specific clock encodings. We then show how to express these problems in terms of qubits, by proving that any QCSP can be reduced to a qubit problem while maintaining the same complexity - something not believed possible classically. The remaining six problems are obtained by considering "sums" and "products" of some of the QSAT problems mentioned here. Before this work, the QSAT problems generated in this way resulted in complete problems for PI and SoPU classes that were trivially equal to NP, MA, or QMA₁. We thus commence the study of these new and seemingly nontrivial classes. While [Meiburg, 2021] first sought to prove completeness for coRP, BQP₁, and QCMA, we note that those constructions are flawed. Here, we rework them, provide correct proofs, and obtain improvements on the required qudit dimensionality.
Cite as

Ricardo Rivera Cardoso, Alex Meiburg, and Daniel Nagaj. Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{riveracardoso_et_al:LIPIcs.TQC.2025.6,
  author =	{Rivera Cardoso, Ricardo and Meiburg, Alex and Nagaj, Daniel},
  title =	{{Quantum SAT Problems with Finite Sets of Projectors Are Complete for a Plethora of Classes}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{6:1--6:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.6},
  URN =		{urn:nbn:de:0030-drops-240557},
  doi =		{10.4230/LIPIcs.TQC.2025.6},
  annote =	{Keywords: Quantum complexity theory, quantum satisfiability, circuit-to-Hamiltonian, pairwise union of classes, pairwise intersection of classes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.77
Minimization of Deterministic Finite Automata Modulo the Edit Distance

Authors: Jakub Michaliszyn and Jan Otop

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

Abstract
We propose a novel approach to minimization of deterministic finite automata (DFA), in which the DFA is further minimized at the expense of relaxing equality of languages to merely a similarity. As the notion of similarity of languages, we consider the edit distance between languages ℒ, ℒ', i.e., the minimal number of edits necessary to transform any word from ℒ to some word from ℒ' and vice versa. In this paper we address two problems: minimization up to a predetermined edit distance given in the input, and minimization up to a bounded edit distance, in which there has to be an upper bound on the number of edits, but it is not specified. We show the first problem to be PSpace {}-complete and that the second problem is in Σ₂^p, and both NP-hard and coNP-hard. We show that if we limit how many strongly connected components can be visited by a single run (i.e., bounded SCC-depth), the problem becomes NP-complete. We also establish maximal subclasses of DFA over which minimization up to a bounded edit distance can be performed in polynomial time. Additionally, we provide a succinct overview of alternative metrics for assessing language similarity.
Cite as

Jakub Michaliszyn and Jan Otop. Minimization of Deterministic Finite Automata Modulo the Edit Distance. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 77:1-77:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{michaliszyn_et_al:LIPIcs.MFCS.2025.77,
  author =	{Michaliszyn, Jakub and Otop, Jan},
  title =	{{Minimization of Deterministic Finite Automata Modulo the Edit Distance}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{77:1--77:17},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-241843},
  doi =		{10.4230/LIPIcs.MFCS.2025.77},
  annote =	{Keywords: automata theory, automata minimization, edit distance}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.25
Blocked Bloom Filters with Choices

Authors: Johanna Elena Schmitz, Jens Zentgraf, and Sven Rahmann

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Probabilistic filters are approximate set membership data structures that represent a set of keys in small space, and answer set membership queries without false negative answers, but with a certain allowed false positive probability. Such filters are widely used in database systems, networks, storage systems and in biological sequence analysis because of their fast query times and low space requirements. Starting with Bloom filters in the 1970s, many filter data structures have been developed, each with its own advantages and disadvantages, e.g., Blocked Bloom filters, Cuckoo filters, XOR filters, Ribbon filters, and more. We introduce Blocked Bloom filters with choices that work similarly to Blocked Bloom filters, except that for each key there are two (or more) alternative choices of blocks where the key’s information may be stored. When inserting a key, we select the block using a cost function which takes into account the current load and the additional number of bits to be set in the candidate blocks. The result is a filter that partially inherits the advantages of a Blocked Bloom filter, such as the ability to insert keys rapidly online or the ability to slightly overload the filter with only a small penalty to the false positive rate. At the same time, it avoids the major disadvantage of a Blocked Bloom filter, namely the larger space consumption. Our new data structure uses less space at the same false positive rate, or has a lower false positive rate at the same space consumption as a Blocked Bloom filter. We discuss the methodology, cost functions for block selection, engineered implementation, a detailed performance evaluation and use cases in bioinformatics of Blocked Bloom filters with choices, showing that they can be of practical value. The implementation of the evaluated filters and the workflows used are provided via Gitlab at https://gitlab.com/rahmannlab/blowchoc-filters.
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Johanna Elena Schmitz, Jens Zentgraf, and Sven Rahmann. Blocked Bloom Filters with Choices. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schmitz_et_al:LIPIcs.SEA.2025.25,
  author =	{Schmitz, Johanna Elena and Zentgraf, Jens and Rahmann, Sven},
  title =	{{Blocked Bloom Filters with Choices}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.25},
  URN =		{urn:nbn:de:0030-drops-232631},
  doi =		{10.4230/LIPIcs.SEA.2025.25},
  annote =	{Keywords: Probabilistic filter, Bloom filter, power of two choices}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.58
A New Impossibility Result for Online Bipartite Matching Problems

Authors: Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani

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

Abstract
Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi [Manshadi et al., 2011] in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio. In this paper we show that no algorithm can achieve a competitive ratio better than 1- e/(e^e) = 0.82062…, improving upon the 0.823 upper bound presented in [Manshadi et al., 2011]. Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1 - 1/e, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.
Cite as

Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani. A New Impossibility Result for Online Bipartite Matching Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chierichetti_et_al:LIPIcs.ICALP.2025.58,
  author =	{Chierichetti, Flavio and Giacchini, Mirko and Panconesi, Alessandro and Vattani, Andrea},
  title =	{{A New Impossibility Result for Online Bipartite Matching Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{58:1--58:20},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-234354},
  doi =		{10.4230/LIPIcs.ICALP.2025.58},
  annote =	{Keywords: Bipartite Matching, Random Graphs, Competitive Ratio}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.10
Count on Your Elders: Laplace vs Gaussian Noise

Authors: Joel Daniel Andersson, Rasmus Pagh, Teresa Anna Steiner, and Sahel Torkamani

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
In recent years, Gaussian noise has become a popular tool in differentially private algorithms, often replacing Laplace noise which dominated the early literature on differential privacy. Gaussian noise is the standard approach to approximate differential privacy, often resulting in much higher utility than traditional (pure) differential privacy mechanisms. In this paper we argue that Laplace noise may in fact be preferable to Gaussian noise in many settings, in particular when we seek to achieve (ε,δ)-differential privacy for small values of δ. We consider two scenarios: First, we consider the problem of counting under continual observation and present a new generalization of the binary tree mechanism that uses a k-ary number system with negative digits to improve the privacy-accuracy trade-off. Our mechanism uses Laplace noise and whenever δ is sufficiently small it improves the mean squared error over the best possible (ε,δ)-differentially private factorization mechanisms based on Gaussian noise. Specifically, using k = 19 we get an asymptotic improvement over the bound given in the work by Henzinger, Upadhyay and Upadhyay (SODA 2023) when δ = O(T^{-0.92}). Second, we show that the noise added by the Gaussian mechanism can always be replaced by Laplace noise of comparable variance for the same (ε, δ)-differential privacy guarantee, and in fact for sufficiently small δ the variance of the Laplace noise becomes strictly better. This challenges the conventional wisdom that Gaussian noise should be used for high-dimensional noise. Finally, we study whether counting under continual observation may be easier in an average-case sense than in a worst-case sense. We show that, under pure differential privacy, the expected worst-case error for a random input must be Ω(log(T)/ε), matching the known lower bound for worst-case inputs.
Cite as

Joel Daniel Andersson, Rasmus Pagh, Teresa Anna Steiner, and Sahel Torkamani. Count on Your Elders: Laplace vs Gaussian Noise. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andersson_et_al:LIPIcs.FORC.2025.10,
  author =	{Andersson, Joel Daniel and Pagh, Rasmus and Steiner, Teresa Anna and Torkamani, Sahel},
  title =	{{Count on Your Elders: Laplace vs Gaussian Noise}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{10:1--10:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.10},
  URN =		{urn:nbn:de:0030-drops-231376},
  doi =		{10.4230/LIPIcs.FORC.2025.10},
  annote =	{Keywords: differential privacy, continual observation, streaming, prefix sums, trees}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.6
Near-Universally-Optimal Differentially Private Minimum Spanning Trees

Authors: Richard Hladík and Jakub Tětek

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being developed to achieve this goal. This makes it very natural to use the notion of universal optimality in differential privacy. Universal optimality is a strong instance-specific optimality guarantee for problems on weighted graphs, which roughly states that for any fixed underlying (unweighted) graph, the algorithm is optimal in the worst-case sense, with respect to the possible setting of the edge weights. In this paper, we give the first such result in differential privacy. Namely, we prove that a simple differentially private mechanism for approximately releasing the minimum spanning tree is near-optimal in the sense of universal optimality for the 𝓁₁ neighbor relation. Previously, it was only known that this mechanism is nearly optimal in the worst case. We then focus on the 𝓁_∞ neighbor relation, for which the described mechanism is not optimal. We show that one may implement the exponential mechanism for MST in polynomial time, and that this results in universal near-optimality for both the 𝓁₁ and the 𝓁_∞ neighbor relations.
Cite as

Richard Hladík and Jakub Tětek. Near-Universally-Optimal Differentially Private Minimum Spanning Trees. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hladik_et_al:LIPIcs.FORC.2025.6,
  author =	{Hlad{\'\i}k, Richard and T\v{e}tek, Jakub},
  title =	{{Near-Universally-Optimal Differentially Private Minimum Spanning Trees}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.6},
  URN =		{urn:nbn:de:0030-drops-231337},
  doi =		{10.4230/LIPIcs.FORC.2025.6},
  annote =	{Keywords: differential privacy, universal optimality, minimum spanning trees}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.49
Cycle Counting Under Local Differential Privacy for Degeneracy-Bounded Graphs

Authors: Quentin Hillebrand, Vorapong Suppakitpaisarn, and Tetsuo Shibuya

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We propose an algorithm for counting the number of cycles under local differential privacy for degeneracy-bounded input graphs. Numerous studies have focused on counting the number of triangles under the privacy notion, demonstrating that the expected 𝓁₂-error of these algorithms is Ω(n^{1.5}), where n is the number of nodes in the graph. When parameterized by the number of cycles of length four (C₄), the best existing triangle counting algorithm has an error of O(n^{1.5} + √C₄) = O(n²). In this paper, we introduce an algorithm with an expected 𝓁₂-error of O(δ^1.5 n^0.5 + δ^0.5 d_max^0.5 n^0.5), where δ is the degeneracy and d_{max} is the maximum degree of the graph. For degeneracy-bounded graphs (δ ∈ Θ(1)) commonly found in practical social networks, our algorithm achieves an expected 𝓁₂-error of O(d_{max}^{0.5} n^{0.5}) = O(n). Our algorithm’s core idea is a precise count of triangles following a preprocessing step that approximately sorts the degree of all nodes. This approach can be extended to approximate the number of cycles of length k, maintaining a similar 𝓁₂-error, namely O(δ^{(k-2)/2} d_max^0.5 n^{(k-2)/2} + δ^{k/2} n^{(k-2)/2}) or O(d_max^0.5 n^{(k-2)/2}) = O(n^{(k-1)/2}) for degeneracy-bounded graphs.
Cite as

Quentin Hillebrand, Vorapong Suppakitpaisarn, and Tetsuo Shibuya. Cycle Counting Under Local Differential Privacy for Degeneracy-Bounded Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hillebrand_et_al:LIPIcs.STACS.2025.49,
  author =	{Hillebrand, Quentin and Suppakitpaisarn, Vorapong and Shibuya, Tetsuo},
  title =	{{Cycle Counting Under Local Differential Privacy for Degeneracy-Bounded Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{49:1--49:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.49},
  URN =		{urn:nbn:de:0030-drops-228748},
  doi =		{10.4230/LIPIcs.STACS.2025.49},
  annote =	{Keywords: Differential privacy, triangle counting, degeneracy, arboricity, graph theory, parameterized accuracy}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.51
Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures

Authors: Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a non-uniform failure model. We introduce the (p,q)-Steiner-Connectivity Preservation problem where we protect a minimum-cost set of edges such that the underlying graph maintains p-edge-connectivity between given terminal pairs against edge failures, assuming at most q unprotected edges can fail. We design polynomial-time exact algorithms for the cases where p and q are small and approximation algorithms for general values of p and q. Additionally, we show that when both p and q are part of the input, even deciding whether a given solution is feasible is NP-complete. This hardness also carries over to Flexible Network Design, a research direction that has gained significant attention. In particular, previous work focuses on problem settings where either p or q is constant, for which our new hardness result now provides justification.
Cite as

Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang. Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 51:1-51:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hommelsheim_et_al:LIPIcs.STACS.2025.51,
  author =	{Hommelsheim, Felix and Liu, Zhenwei and Megow, Nicole and Zhang, Guochuan},
  title =	{{Protecting the Connectivity of a Graph Under Non-Uniform Edge Failures}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{51:1--51:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.51},
  URN =		{urn:nbn:de:0030-drops-228761},
  doi =		{10.4230/LIPIcs.STACS.2025.51},
  annote =	{Keywords: Network Design, Edge Failures, Graph Connectivity, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.64
A Universal Sequence of Tensors for the Asymptotic Rank Conjecture

Authors: Petteri Kaski and Mateusz Michałek

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

Abstract
The exponent σ(T) of a tensor T ∈ 𝔽^d⊗𝔽^d⊗𝔽^d over a field 𝔽 captures the base of the exponential growth rate of the tensor rank of T under Kronecker powers. Tensor exponents are fundamental from the standpoint of algorithms and computational complexity theory; for example, the exponent ω of square matrix multiplication can be characterized as ω = 2σ(MM₂), where MM₂ ∈ 𝔽⁴⊗𝔽⁴⊗𝔽⁴ is the tensor that represents 2×2 matrix multiplication. Strassen [FOCS 1986] initiated a duality theory for spaces of tensors that enables one to characterize the exponent of a tensor via objects in a dual space, called the asymptotic spectrum of the primal (tensor) space. While Strassen’s theory has considerable generality beyond the setting of tensors - Wigderson and Zuiddam [Asymptotic Spectra: Theory, Applications, and Extensions, preprint, 2023] give a recent exposition - progress in characterizing the dual space in the tensor setting has been slow, with the first universal points in the dual identified by Christandl, Vrana, and Zuiddam [J. Amer. Math. Soc. 36 (2023)]. In parallel to Strassen’s theory, the algebraic geometry community has developed a geometric theory of tensors aimed at characterizing the structure of the primal space and tensor exponents therein; the latter study was motivated in particular by an observation of Strassen (implicit in [J. Reine Angew. Math. 384 (1988)]) that matrix-multiplication tensors have limited universality in the sense that σ(𝔽^d⊗𝔽^d⊗𝔽^d) ≤ 2ω/3 = 4/3σ(MM₂) holds for all d ≥ 1. In particular, this limited universality of the tensor MM₂ puts forth the question whether one could construct explicit universal tensors that exactly characterize the worst-case tensor exponent in the primal space. Such explicit universal objects would, among others, give means towards a proof or a disproof of Strassen’s asymptotic rank conjecture [Progr. Math. 120 (1994)]; the former would immediately imply ω = 2 and, among others, refute the Set Cover Conjecture (cf. Björklund and Kaski [STOC 2024] and Pratt [STOC 2024]). Our main result is an explicit construction of a sequence 𝒰_d of zero-one-valued tensors that is universal for the worst-case tensor exponent; more precisely, we show that σ(𝒰_d) = σ(d) where σ(d) = sup_{T ∈ 𝔽^d⊗𝔽^d⊗𝔽^d}σ(T). We also supply an explicit universal sequence 𝒰_Δ localised to capture the worst-case exponent σ(Δ) of tensors with support contained in Δ ⊆ [d]×[d]×[d]; by combining such sequences, we obtain a universal sequence 𝒯_d such that σ(𝒯_d) = 1 holds if and only if Strassen’s asymptotic rank conjecture holds for d. Finally, we show that the limit lim_{d → ∞}σ(d) exists and can be captured as lim_{d → ∞} σ(D_d) for an explicit sequence (D_d)_{d = 1}^∞ of tensors obtained by diagonalisation of the sequences 𝒰_d. As our second result we relate the absence of polynomials of fixed degree vanishing on tensors of low rank, or more generally asymptotic rank, with upper bounds on the exponent σ(d). Using this technique, one may bound asymptotic rank for all tensors of a given format, knowing enough specific tensors of low asymptotic rank.
Cite as

Petteri Kaski and Mateusz Michałek. A Universal Sequence of Tensors for the Asymptotic Rank Conjecture. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 64:1-64:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kaski_et_al:LIPIcs.ITCS.2025.64,
  author =	{Kaski, Petteri and Micha{\l}ek, Mateusz},
  title =	{{A Universal Sequence of Tensors for the Asymptotic Rank Conjecture}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{64:1--64:24},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-226925},
  doi =		{10.4230/LIPIcs.ITCS.2025.64},
  annote =	{Keywords: asymptotic rank conjecture, secant variety, Specht module, tensor rank, tensor exponent}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.67
Error-Correcting Graph Codes

Authors: Swastik Kopparty, Aditya Potukuchi, and Harry Sha

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

Abstract
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance δ is a family C of graphs, on a common vertex set of size n, such that if we start with any graph in C, we would have to modify the neighborhoods of at least δ n vertices in order to obtain some other graph in C. This is a natural graph generalization of the standard Hamming distance error-correcting codes for binary strings. Yohananov and Yaakobi were the first to construct codes in this metric. We extend their work by showing 1) Combinatorial results determining the optimal rate vs distance trade-off nonconstructively. 2) Graph code analogues of Reed-Solomon codes and code concatenation, leading to positive distance codes for all rates and positive rate codes for all distances. 3) Graph code analogues of dual-BCH codes, yielding large codes with distance δ = 1-o(1). This gives an explicit "graph code of Ramsey graphs". Several recent works, starting with the paper of Alon, Gujgiczer, Körner, Milojević, and Simonyi, have studied more general graph codes; where the symmetric difference between any two graphs in the code is required to have some desired property. Error-correcting graph codes are a particularly interesting instantiation of this concept.
Cite as

Swastik Kopparty, Aditya Potukuchi, and Harry Sha. Error-Correcting Graph Codes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kopparty_et_al:LIPIcs.ITCS.2025.67,
  author =	{Kopparty, Swastik and Potukuchi, Aditya and Sha, Harry},
  title =	{{Error-Correcting Graph Codes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{67:1--67:20},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-226950},
  doi =		{10.4230/LIPIcs.ITCS.2025.67},
  annote =	{Keywords: Graph codes, explicit construction, concatenation codes, tensor codes}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.25
Chopin: Combining Distributed and Centralized Schedulers for Self-Adjusting Datacenter Networks

Authors: Neta Rozen-Schiff, Klaus-Tycho Foerster, Stefan Schmid, and David Hay

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
The performance of distributed and data-centric applications often critically depends on the interconnecting network. Emerging reconfigurable datacenter networks (RDCNs) are a particularly innovative approach to improve datacenter throughput. Relying on a dynamic optical topology which can be adjusted towards the workload in a demand-aware manner, RDCNs allow to exploit temporal and spatial locality in the communication pattern, and to provide topological shortcuts for frequently communicating racks. The key challenge, however, concerns how to realize demand-awareness in RDCNs in a scalable fashion. This paper presents and evaluates Chopin, a hybrid scheduler for self-adjusting networks that provides demand-awareness at low overhead, by combining centralized and distributed approaches. Chopin allocates optical circuits to elephant flows, through its slower centralized scheduler, utilizing global information. Chopin’s distributed scheduler is orders of magnitude faster and can swiftly react to changes in the traffic and adjust the optical circuits accordingly, by using only local information and running at each rack separately.
Cite as

Neta Rozen-Schiff, Klaus-Tycho Foerster, Stefan Schmid, and David Hay. Chopin: Combining Distributed and Centralized Schedulers for Self-Adjusting Datacenter Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rozenschiff_et_al:LIPIcs.OPODIS.2022.25,
  author =	{Rozen-Schiff, Neta and Foerster, Klaus-Tycho and Schmid, Stefan and Hay, David},
  title =	{{Chopin: Combining Distributed and Centralized Schedulers for Self-Adjusting Datacenter Networks}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{25:1--25:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.25},
  URN =		{urn:nbn:de:0030-drops-176457},
  doi =		{10.4230/LIPIcs.OPODIS.2022.25},
  annote =	{Keywords: reconfigurable optical networks, centralized scheduler, distributed scheduler}
}
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