69 Search Results for "D�ck, Stefan"

Document
DOI: 10.4230/DagRep.13.11.72
Space and Artificial Intelligence (Dagstuhl Seminar 23461)

Authors: Sašo Džeroski, Holger H. Hoos, Bertrand Le Saux, Leendert van der Torre, and Ana Kostovska

Published in: Dagstuhl Reports, Volume 13, Issue 11 (2024)

Abstract
This report documents the program and the outcomes of the Dagstuhl Seminar 23461 "Space and Artificial Intelligence". The seminar was interdisciplinary, situated at the intersection of research on AI / computer science and space research. Since each of these is a very wide field on its own, we focussed on a selection of topics from each of the two and their intersections. On the artificial intelligence side, we focused on data-driven AI, which makes use of data in order to produce intelligent behaviour and notably includes machine learning approaches. We also considered knowledge-based AI, which is focussed on the explicit formalisation of human knowledge and its use for tasks such as reasoning, planning, and scheduling. On the space research side, we considered the two major branches of space operations (SO) and Earth observation (EO). The seminar brought together a diverse set of players, including researchers from academia, on one hand, and practitioners from space agencies (ESA, NASA) and industry, on the other hand. The seminar included plenary talks and parallel group discussions. Through the plenary talks, we obtained insight into the state-of-the-art in the different areas of AI research and space research, and especially in their intersections. Through the parallel group discussions, we identified obstacles and challenges to further progress and charted directions for further work.
Cite as

Sašo Džeroski, Holger H. Hoos, Bertrand Le Saux, Leendert van der Torre, and Ana Kostovska. Space and Artificial Intelligence (Dagstuhl Seminar 23461). In Dagstuhl Reports, Volume 13, Issue 11, pp. 72-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{dzeroski_et_al:DagRep.13.11.72,
  author =	{D\v{z}eroski, Sa\v{s}o and Hoos, Holger H. and Le Saux, Bertrand and van der Torre, Leendert and Kostovska, Ana},
  title =	{{Space and Artificial Intelligence (Dagstuhl Seminar 23461)}},
  pages =	{72--102},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{11},
  editor =	{D\v{z}eroski, Sa\v{s}o and Hoos, Holger H. and Le Saux, Bertrand and van der Torre, Leendert and Kostovska, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.11.72},
  URN =		{urn:nbn:de:0030-drops-198454},
  doi =		{10.4230/DagRep.13.11.72},
  annote =	{Keywords: Artificial Intelligence, Machine Learning, Data-based AI, Knowledge-based AI, Deep Learning, Foundation Models, Explainable Artificial Intelligence, Space Research, Space Operations, Earth Observation}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2023.11
On the Convergence Time in Graphical Games: A Locality-Sensitive Approach

Authors: Juho Hirvonen, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract
Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though an agent’s payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with constant-round local algorithms. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood.
Cite as

Juho Hirvonen, Laura Schmid, Krishnendu Chatterjee, and Stefan Schmid. On the Convergence Time in Graphical Games: A Locality-Sensitive Approach. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hirvonen_et_al:LIPIcs.OPODIS.2023.11,
  author =	{Hirvonen, Juho and Schmid, Laura and Chatterjee, Krishnendu and Schmid, Stefan},
  title =	{{On the Convergence Time in Graphical Games: A Locality-Sensitive Approach}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.11},
  URN =		{urn:nbn:de:0030-drops-195015},
  doi =		{10.4230/LIPIcs.OPODIS.2023.11},
  annote =	{Keywords: distributed computing, Nash equilibria, mechanism design, best-response dynamics}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.17
An Extension Theorem for Signotopes

Authors: Helena Bergold, Stefan Felsner, and Manfred Scheucher

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
In 1926, Levi showed that, for every pseudoline arrangement 𝒜 and two points in the plane, 𝒜 can be extended by a pseudoline which contains the two prescribed points. Later extendability was studied for arrangements of pseudohyperplanes in higher dimensions. While the extendability of an arrangement of proper hyperplanes in ℝ^d with a hyperplane containing d prescribed points is trivial, Richter-Gebert found an arrangement of pseudoplanes in ℝ³ which cannot be extended with a pseudoplane containing two particular prescribed points. In this article, we investigate the extendability of signotopes, which are a combinatorial structure encoding a rich subclass of pseudohyperplane arrangements. Our main result is that signotopes of odd rank are extendable in the sense that for two prescribed crossing points we can add an element containing them. Moreover, we conjecture that in all even ranks r ≥ 4 there exist signotopes which are not extendable for two prescribed points. Our conjecture is supported by examples in ranks 4, 6, 8, 10, and 12 that were found with a SAT based approach.
Cite as

Helena Bergold, Stefan Felsner, and Manfred Scheucher. An Extension Theorem for Signotopes. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bergold_et_al:LIPIcs.SoCG.2023.17,
  author =	{Bergold, Helena and Felsner, Stefan and Scheucher, Manfred},
  title =	{{An Extension Theorem for Signotopes}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.17},
  URN =		{urn:nbn:de:0030-drops-178676},
  doi =		{10.4230/LIPIcs.SoCG.2023.17},
  annote =	{Keywords: arrangement of pseudolines, extendability, Levi’s extension lemma, arrangement of pseudohyperplanes, signotope, oriented matroid, partial order, Boolean satisfiability (SAT)}
}
Document
DOI: 10.4230/OASIcs.EVCS.2023.5
Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics

Authors: Houda Boukham, Guido Wachsmuth, Toine Hartman, Hamza Boucherit, Oskar van Rest, Hassan Chafi, Sungpack Hong, Martijn Dwars, Arnaud Delamare, and Dalila Chiadmi

Published in: OASIcs, Volume 109, Eelco Visser Commemorative Symposium (EVCS 2023)

Abstract
For the last decade, teams at Oracle relied on the Spoofax language workbench to develop a family of domain-specific languages for graph analytics in research projects and in product development. In this paper, we analyze the requirements for integrating language processors into large-scale graph analytics toolkits and for the development of these language processors as part of a larger product development process. We discuss how Spoofax helps to meet these requirements and point out the need for future improvements.
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Houda Boukham, Guido Wachsmuth, Toine Hartman, Hamza Boucherit, Oskar van Rest, Hassan Chafi, Sungpack Hong, Martijn Dwars, Arnaud Delamare, and Dalila Chiadmi. Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics. In Eelco Visser Commemorative Symposium (EVCS 2023). Open Access Series in Informatics (OASIcs), Volume 109, pp. 5:1-5:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boukham_et_al:OASIcs.EVCS.2023.5,
  author =	{Boukham, Houda and Wachsmuth, Guido and Hartman, Toine and Boucherit, Hamza and van Rest, Oskar and Chafi, Hassan and Hong, Sungpack and Dwars, Martijn and Delamare, Arnaud and Chiadmi, Dalila},
  title =	{{Spoofax at Oracle: Domain-Specific Language Engineering for Large-Scale Graph Analytics}},
  booktitle =	{Eelco Visser Commemorative Symposium (EVCS 2023)},
  pages =	{5:1--5:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-267-9},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{109},
  editor =	{L\"{a}mmel, Ralf and Mosses, Peter D. and Steimann, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.EVCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-177756},
  doi =		{10.4230/OASIcs.EVCS.2023.5},
  annote =	{Keywords: language workbench, domain-specific language}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.10
Efficiently Testable Circuits

Authors: Mirza Ahad Baig, Suvradip Chakraborty, Stefan Dziembowski, Małgorzata Gałązka, Tomasz Lizurej, and Krzysztof Pietrzak

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

Abstract
In this work, we put forward the notion of "efficiently testable circuits" and provide circuit compilers that transform any circuit into an efficiently testable one. Informally, a circuit is testable if one can detect tampering with the circuit by evaluating it on a small number of inputs from some test set. Our technical contribution is a compiler that transforms any circuit C into a testable circuit (Ĉ,𝕋̂) for which we can detect arbitrary tampering with all wires in Ĉ. The notion of a testable circuit is weaker or incomparable to existing notions of tamper-resilience, which aim to detect or even correct for errors introduced by tampering during every query, but our new notion is interesting in several settings, and we achieve security against much more general tampering classes - like tampering with all wires - with very modest overhead. Concretely, starting from a circuit C of size n and depth d, for any L (think of L as a small constant, say L = 4), we get a testable (Ĉ,𝕋̂) where Ĉ is of size ≈ 12n and depth d+log(n)+L⋅ n^{1/L}. The test set 𝕋̂ is of size 4⋅ 2^L. The number of extra input and output wires (i.e., pins) we need to add for the testing is 3+L and 2^L, respectively.
Cite as

Mirza Ahad Baig, Suvradip Chakraborty, Stefan Dziembowski, Małgorzata Gałązka, Tomasz Lizurej, and Krzysztof Pietrzak. Efficiently Testable Circuits. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baig_et_al:LIPIcs.ITCS.2023.10,
  author =	{Baig, Mirza Ahad and Chakraborty, Suvradip and Dziembowski, Stefan and Ga{\l}\k{a}zka, Ma{\l}gorzata and Lizurej, Tomasz and Pietrzak, Krzysztof},
  title =	{{Efficiently Testable Circuits}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{10:1--10:23},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.10},
  URN =		{urn:nbn:de:0030-drops-175130},
  doi =		{10.4230/LIPIcs.ITCS.2023.10},
  annote =	{Keywords: circuit compilers, circuit integrity, circuit testing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.14
An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions

Authors: Florian Barth, Stefan Funke, and Claudius Proissl

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Graphs with multiple edge costs arise naturally in the route planning domain when apart from travel time other criteria like fuel consumption or positive height difference are also objectives to be minimized. In such a scenario, this paper investigates the number of extreme shortest paths between a given source-target pair s, t. We show that for a fixed but arbitrary number of cost types d ≥ 1 the number of extreme shortest paths is in n^O(log^{d-1}n) in graphs G with n nodes. This is a generalization of known upper bounds for d = 2 and d = 3.
Cite as

Florian Barth, Stefan Funke, and Claudius Proissl. An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{barth_et_al:LIPIcs.ESA.2022.14,
  author =	{Barth, Florian and Funke, Stefan and Proissl, Claudius},
  title =	{{An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{14:1--14:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.14},
  URN =		{urn:nbn:de:0030-drops-169525},
  doi =		{10.4230/LIPIcs.ESA.2022.14},
  annote =	{Keywords: Parametric Shortest Paths, Extreme Shortest Paths}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.47
Finding a Cluster in Incomplete Data

Authors: Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study two variants of the fundamental problem of finding a cluster in incomplete data. In the problems under consideration, we are given a multiset of incomplete d-dimensional vectors over the binary domain and integers k and r, and the goal is to complete the missing vector entries so that the multiset of complete vectors either contains (i) a cluster of k vectors of radius at most r, or (ii) a cluster of k vectors of diameter at most r. We give tight characterizations of the parameterized complexity of the problems under consideration with respect to the parameters k, r, and a third parameter that captures the missing vector entries.
Cite as

Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider. Finding a Cluster in Incomplete Data. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{eiben_et_al:LIPIcs.ESA.2022.47,
  author =	{Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ordyniak, Sebastian and Szeider, Stefan},
  title =	{{Finding a Cluster in Incomplete Data}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.47},
  URN =		{urn:nbn:de:0030-drops-169858},
  doi =		{10.4230/LIPIcs.ESA.2022.47},
  annote =	{Keywords: Parameterized complexity, incomplete data, clustering}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.COSIT.2022.25
Collaborative Wayfinding Under Distributed Spatial Knowledge (Short Paper)

Authors: Panagiotis Mavros, Saskia Kuliga, Ed Manley, Hilal Rohaidi Fitri, Michael Joos, and Christoph Hölscher

Published in: LIPIcs, Volume 240, 15th International Conference on Spatial Information Theory (COSIT 2022)

Abstract
In many everyday situations, two or more people navigate collaboratively but their spatial knowledge does not necessarily overlap. However, most research to date, has investigated social wayfinding under either 1-sided or fully shared spatial information. Here, we present the pilot experiment of a novel, computerised, non-verbal experimental paradigm to study collaborative wayfinding under the face of spatial information uncertainty. Participants (N=32) learned two different neighbourhoods individually, and then navigated together as dyads (D=16), from one neighbourhood to the other. Our pilot results reveal that overall participants share navigational control, but are in control more when the task leads them to a familiar destination. We discuss the effects of spatial ability and motivation to lead, as well as the outlook of the paradigm.
Cite as

Panagiotis Mavros, Saskia Kuliga, Ed Manley, Hilal Rohaidi Fitri, Michael Joos, and Christoph Hölscher. Collaborative Wayfinding Under Distributed Spatial Knowledge (Short Paper). In 15th International Conference on Spatial Information Theory (COSIT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 240, pp. 25:1-25:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mavros_et_al:LIPIcs.COSIT.2022.25,
  author =	{Mavros, Panagiotis and Kuliga, Saskia and Manley, Ed and Fitri, Hilal Rohaidi and Joos, Michael and H\"{o}lscher, Christoph},
  title =	{{Collaborative Wayfinding Under Distributed Spatial Knowledge}},
  booktitle =	{15th International Conference on Spatial Information Theory (COSIT 2022)},
  pages =	{25:1--25:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-257-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{240},
  editor =	{Ishikawa, Toru and Fabrikant, Sara Irina and Winter, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2022.25},
  URN =		{urn:nbn:de:0030-drops-169105},
  doi =		{10.4230/LIPIcs.COSIT.2022.25},
  annote =	{Keywords: navigation, wayfinding, collaboration, dyad, online}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2022.1
Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms (Invited Talk)

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long paths in graphs. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d > 1, is either Hamiltonian or contains a cycle of length at least 2d. Second, the theorem of Erdős-Gallai from 1959, states that a graph G with the average vertex degree D > 1, contains a cycle of length at least D. The proofs of these theorems are constructive, they provide polynomial-time algorithms constructing cycles of lengths 2d and D. We extend these algorithmic results by showing that each of the problems, to decide whether a 2-connected graph contains a cycle of length at least 2d+k or of a cycle of length at least D+k, is fixed-parameter tractable parameterized by k.
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms (Invited Talk). In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fomin_et_al:LIPIcs.MFCS.2022.1,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Long Cycles in Graphs: Extremal Combinatorics Meets Parameterized Algorithms}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{1:1--1:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.1},
  URN =		{urn:nbn:de:0030-drops-167999},
  doi =		{10.4230/LIPIcs.MFCS.2022.1},
  annote =	{Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, dense graph, Dirac theorem, Erd\H{o}s-Gallai theorem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.8
The Complexity of Periodic Energy Minimisation

Authors: Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, and Igor Potapov

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
The computational complexity of pairwise energy minimisation of N points in real space is a long-standing open problem. The idea of the potential intractability of the problem was supported by a lack of progress in finding efficient algorithms, even when restricted the integer grid approximation. In this paper we provide a firm answer to the problem on ℤ^d by showing that for a large class of pairwise energy functions the problem of periodic energy minimisation is NP-hard if the size of the period (known as a unit cell) is fixed, and is undecidable otherwise. We do so by introducing an abstraction of pairwise average energy minimisation as a mathematical problem, which covers many existing models. The most influential aspects of this work are showing for the first time: 1) undecidability of average pairwise energy minimisation in general 2) computational hardness for the most natural model with periodic boundary conditions, and 3) novel reductions for a large class of generic pairwise energy functions covering many physical abstractions at once. In particular, we develop a new tool of overlapping digital rhombuses to incorporate the properties of the physical force fields, and we connect it with classical tiling problems. Moreover, we illustrate the power of such reductions by incorporating more physical properties such as charge neutrality, and we show an inapproximability result for the extreme case of the 1D average energy minimisation problem.
Cite as

Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, and Igor Potapov. The Complexity of Periodic Energy Minimisation. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{adamson_et_al:LIPIcs.MFCS.2022.8,
  author =	{Adamson, Duncan and Deligkas, Argyrios and Gusev, Vladimir V. and Potapov, Igor},
  title =	{{The Complexity of Periodic Energy Minimisation}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.8},
  URN =		{urn:nbn:de:0030-drops-168065},
  doi =		{10.4230/LIPIcs.MFCS.2022.8},
  annote =	{Keywords: Optimisation of periodic structures, tiling, undecidability, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.13
Graph Realization of Distance Sets

Authors: Amotz Bar-Noy, David Peleg, Mor Perry, and Dror Rawitz

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
The Distance Realization problem is defined as follows. Given an n × n matrix D of nonnegative integers, interpreted as inter-vertex distances, find an n-vertex weighted or unweighted graph G realizing D, i.e., whose inter-vertex distances satisfy dist_G(i,j) = D_{i,j} for every 1 ≤ i < j ≤ n, or decide that no such realizing graph exists. The problem was studied for general weighted and unweighted graphs, as well as for cases where the realizing graph is restricted to a specific family of graphs (e.g., trees or bipartite graphs). An extension of Distance Realization that was studied in the past is where each entry in the matrix D may contain a range of consecutive permissible values. We refer to this extension as Range Distance Realization (or Range-DR). Restricting each range to at most k values yields the problem k-Range Distance Realization (or k-Range-DR). The current paper introduces a new extension of Distance Realization, in which each entry D_{i,j} of the matrix may contain an arbitrary set of acceptable values for the distance between i and j, for every 1 ≤ i < j ≤ n. We refer to this extension as Set Distance Realization (Set-DR), and to the restricted problem where each entry may contain at most k values as k-Set Distance Realization (or k-Set-DR). We first show that 2-Range-DR is NP-hard for unweighted graphs (implying the same for 2-Set-DR). Next we prove that 2-Set-DR is NP-hard for unweighted and weighted trees. We then explore Set-DR where the realization is restricted to the families of stars, paths, or cycles. For the weighted case, our positive results are that for each of these families there exists a polynomial time algorithm for 2-Set-DR. On the hardness side, we prove that 6-Set-DR is NP-hard for stars and 5-Set-DR is NP-hard for paths and cycles. For the unweighted case, our results are the same, except for the case of unweighted stars, for which k-Set-DR is polynomially solvable for any k.
Cite as

Amotz Bar-Noy, David Peleg, Mor Perry, and Dror Rawitz. Graph Realization of Distance Sets. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{barnoy_et_al:LIPIcs.MFCS.2022.13,
  author =	{Bar-Noy, Amotz and Peleg, David and Perry, Mor and Rawitz, Dror},
  title =	{{Graph Realization of Distance Sets}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.13},
  URN =		{urn:nbn:de:0030-drops-168119},
  doi =		{10.4230/LIPIcs.MFCS.2022.13},
  annote =	{Keywords: Graph Realization, distance realization, network design}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.17
Fixed-Point Cycles and Approximate EFX Allocations

Authors: Benjamin Aram Berendsohn, Simona Boyadzhiyska, and László Kozma

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We study edge-labelings of the complete bidirected graph K^↔_n with functions that map the set [d] = {1, … , d} to itself. We call a directed cycle in K^↔_n a fixed-point cycle if composing the labels of its edges in order results in a map that has a fixed point, and we say that a labeling is fixed-point-free if no fixed-point cycle exists. For a given d, we ask for the largest value of n, denoted R_f(d), for which there exists a fixed-point-free labeling of K^↔_n. Determining R_f(d) for all d > 0 is a natural Ramsey-type question, generalizing some well-studied zero-sum problems in extremal combinatorics. The problem was recently introduced by Chaudhury, Garg, Mehlhorn, Mehta, and Misra [EC 2021], who proved that d ≤ R_f(d) ≤ d⁴+d and showed that the problem has close connections to EFX allocations, a central problem of fair allocation in social choice theory. In this paper we show the improved bound R_f(d) ≤ d^{2 + o(1)}, yielding an efficient (1-ε)-EFX allocation with n agents and O((n/ε)^{0.67}) unallocated goods; this improves the bound of O((n/ε)^{0.8}) of Chaudhury, Garg, Mehlhorn, Mehta, and Misra. {Additionally, we prove the stronger upper bound 2d-2, in the case where all edge-labels are permutations. A very special case of this problem, that of finding zero-sum cycles in digraphs whose edges are labeled with elements of ℤ_d, was recently considered by Alon and Krivelevich [JGT 2021] and by Mészáros and Steiner [EJC 2021]. Our result improves the bounds obtained by these authors and extends them to labelings with elements of an arbitrary (not necessarily commutative) group, while also simplifying the proof.}
Cite as

Benjamin Aram Berendsohn, Simona Boyadzhiyska, and László Kozma. Fixed-Point Cycles and Approximate EFX Allocations. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{berendsohn_et_al:LIPIcs.MFCS.2022.17,
  author =	{Berendsohn, Benjamin Aram and Boyadzhiyska, Simona and Kozma, L\'{a}szl\'{o}},
  title =	{{Fixed-Point Cycles and Approximate EFX Allocations}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.17},
  URN =		{urn:nbn:de:0030-drops-168153},
  doi =		{10.4230/LIPIcs.MFCS.2022.17},
  annote =	{Keywords: fixed-point, zero-sum cycle, Ramsey theory, fair allocation, EFX}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.18
Improved Lower Bound, and Proof Barrier, for Constant Depth Algebraic Circuits

Authors: C. S. Bhargav, Sagnik Dutta, and Nitin Saxena

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We show that any product-depth Δ algebraic circuit for the Iterated Matrix Multiplication Polynomial IMM_{n,d} (when d = O(log n/log log n)) must be of size at least n^Ω(d^{1/(φ²)^Δ}) where φ = 1.618… is the golden ratio. This improves the recent breakthrough result of Limaye, Srinivasan and Tavenas (FOCS'21) who showed a super polynomial lower bound of the form n^Ω(d^{1/4^Δ}) for constant-depth circuits. One crucial idea of the (LST21) result was to use set-multilinear polynomials where each of the sets in the underlying partition of the variables could be of different sizes. By picking the set sizes more carefully (depending on the depth we are working with), we first show that any product-depth Δ set-multilinear circuit for IMM_{n,d} (when d = O(log n)) needs size at least n^Ω(d^{1/φ^Δ}). This improves the n^Ω(d^{1/2^Δ}) lower bound of (LST21). We then use their Hardness Escalation technique to lift this to general circuits. We also show that our lower bound cannot be improved significantly using these same techniques. For the specific two set sizes used in (LST21), they showed that their lower bound cannot be improved. We show that for any d^o(1) set sizes (out of maximum possible d), the scope for improving our lower bound is minuscule: there exists a set-multilinear circuit that has product-depth Δ and size almost matching our lower bound such that the value of the measure used to prove the lower bound is maximum for this circuit. This results in a barrier to further improvement using the same measure.
Cite as

C. S. Bhargav, Sagnik Dutta, and Nitin Saxena. Improved Lower Bound, and Proof Barrier, for Constant Depth Algebraic Circuits. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhargav_et_al:LIPIcs.MFCS.2022.18,
  author =	{Bhargav, C. S. and Dutta, Sagnik and Saxena, Nitin},
  title =	{{Improved Lower Bound, and Proof Barrier, for Constant Depth Algebraic Circuits}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.18},
  URN =		{urn:nbn:de:0030-drops-168161},
  doi =		{10.4230/LIPIcs.MFCS.2022.18},
  annote =	{Keywords: polynomials, lower bounds, algebraic circuits, proof barrier, fibonacci numbers}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.29
On Kernels for d-Path Vertex Cover

Authors: Radovan Červený, Pratibha Choudhary, and Ondřej Suchý

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
In this paper we study the kernelization of the d-Path Vertex Cover (d-PVC) problem. Given a graph G, the problem requires finding whether there exists a set of at most k vertices whose removal from G results in a graph that does not contain a path (not necessarily induced) with d vertices. It is known that d-PVC is NP-complete for d ≥ 2. Since the problem generalizes to d-Hitting Set, it is known to admit a kernel with 𝒪(dk^d) edges. We improve on this by giving better kernels. Specifically, we give kernels with 𝒪(k²) vertices and edges for the cases when d = 4 and d = 5. Further, we give a kernel with 𝒪(k⁴d^{2d+9}) vertices and edges for general d.
Cite as

Radovan Červený, Pratibha Choudhary, and Ondřej Suchý. On Kernels for d-Path Vertex Cover. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cerveny_et_al:LIPIcs.MFCS.2022.29,
  author =	{\v{C}erven\'{y}, Radovan and Choudhary, Pratibha and Such\'{y}, Ond\v{r}ej},
  title =	{{On Kernels for d-Path Vertex Cover}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.29},
  URN =		{urn:nbn:de:0030-drops-168279},
  doi =		{10.4230/LIPIcs.MFCS.2022.29},
  annote =	{Keywords: Parameterized complexity, Kernelization, d-Hitting Set, d-Path Vertex Cover, Expansion Lemma}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.31
Sample Compression Schemes for Balls in Graphs

Authors: Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O(d). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r, we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ-hyperbolic graphs.
Cite as

Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès. Sample Compression Schemes for Balls in Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chalopin_et_al:LIPIcs.MFCS.2022.31,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Mc Inerney, Fionn and Ratel, S\'{e}bastien and Vax\`{e}s, Yann},
  title =	{{Sample Compression Schemes for Balls in Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.31},
  URN =		{urn:nbn:de:0030-drops-168298},
  doi =		{10.4230/LIPIcs.MFCS.2022.31},
  annote =	{Keywords: Proper Sample Compression Schemes, Balls, Graphs, VC-dimension}
}
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