23 Search Results for "David, Nicolas"

Document
DOI: 10.4230/LIPIcs.TIME.2024.5
Open the Chests: An Environment for Activity Recognition and Sequential Decision Problems Using Temporal Logic

Authors: Ivelina Stoyanova, Nicolas Museux, Sao Mai Nguyen, and David Filliat

Published in: LIPIcs, Volume 318, 31st International Symposium on Temporal Representation and Reasoning (TIME 2024)

Abstract
This article presents Open the Chests, a novel benchmark environment designed for simulating and testing activity recognition and reactive decision-making algorithms. By leveraging temporal logic, Open the Chests offers a dynamic, event-driven simulation platform that illustrates the complexities of real-world systems. The environment contains multiple chests, each representing an activity pattern that an interacting agent must identify and respond to by pressing a corresponding button. The agent must analyze sequences of asynchronous events generated by the environment to recognize these patterns and make informed decisions. With the aim of theoretically grounding the environment, the Activity-Based Markov Decision Process (AB-MDP) is defined, allowing to model the context-dependent interaction with activities. Our goal is to propose a robust tool for the development, testing, and bench-marking of algorithms that is illustrative of realistic scenarios and allows for the isolation of specific complexities in event-driven environments.
Cite as

Ivelina Stoyanova, Nicolas Museux, Sao Mai Nguyen, and David Filliat. Open the Chests: An Environment for Activity Recognition and Sequential Decision Problems Using Temporal Logic. In 31st International Symposium on Temporal Representation and Reasoning (TIME 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 318, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{stoyanova_et_al:LIPIcs.TIME.2024.5,
  author =	{Stoyanova, Ivelina and Museux, Nicolas and Nguyen, Sao Mai and Filliat, David},
  title =	{{Open the Chests: An Environment for Activity Recognition and Sequential Decision Problems Using Temporal Logic}},
  booktitle =	{31st International Symposium on Temporal Representation and Reasoning (TIME 2024)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-349-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{318},
  editor =	{Sala, Pietro and Sioutis, Michael and Wang, Fusheng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2024.5},
  URN =		{urn:nbn:de:0030-drops-212128},
  doi =		{10.4230/LIPIcs.TIME.2024.5},
  annote =	{Keywords: Event-Based Decision Making, Activity Recognition, Temporal Logic, Reinforcement Learning, Dynamic Systems, Complex Event Processing, Benchmark Environment, Real-Time Simulation}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.COSIT.2024.21
An Ontology and Geospatial Knowledge Graph for Reasoning About Cascading Failures (Short Paper)

Authors: Torsten Hahmann and David K. Kedrowski

Published in: LIPIcs, Volume 315, 16th International Conference on Spatial Information Theory (COSIT 2024)

Abstract
During a natural disaster such as flooding, the failure of a single asset in the complex and interconnected web of critical urban infrastructure can trigger a cascade of failures within and across multiple systems with potentially life-threatening consequences. To help emergency management effectively and efficiently assess such failures, we design the Utility Connection Ontology Design Pattern to represent utility services and model connections within and across those services. The pattern is encoded as an OWL ontology and instantiated with utility data in a geospatial knowledge graph. We demonstrate how it facilitates reasoning to identify cascading service failures due to flooding for producing maps and other summaries for situational awareness.
Cite as

Torsten Hahmann and David K. Kedrowski. An Ontology and Geospatial Knowledge Graph for Reasoning About Cascading Failures (Short Paper). In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 21:1-21:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hahmann_et_al:LIPIcs.COSIT.2024.21,
  author =	{Hahmann, Torsten and Kedrowski, David K.},
  title =	{{An Ontology and Geospatial Knowledge Graph for Reasoning About Cascading Failures}},
  booktitle =	{16th International Conference on Spatial Information Theory (COSIT 2024)},
  pages =	{21:1--21:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-330-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{315},
  editor =	{Adams, Benjamin and Griffin, Amy L. and Scheider, Simon and McKenzie, Grant},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2024.21},
  URN =		{urn:nbn:de:0030-drops-208364},
  doi =		{10.4230/LIPIcs.COSIT.2024.21},
  annote =	{Keywords: knowledge graph, ontology, OWL, spatial reasoning, cascading failures, urban infrastructure}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.14
End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation

Authors: Florian Faissole, Paul Geneau de Lamarlière, and Guillaume Melquiond

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Designing an efficient yet accurate floating-point approximation of a mathematical function is an intricate and error-prone process. This warrants the use of formal methods, especially formal proof, to achieve some degree of confidence in the implementation. Unfortunately, the lack of automation or its poor interplay with the more manual parts of the proof makes it way too costly in practice. This article revisits the issue by proposing a methodology and some dedicated automation, and applies them to the use case of a faithful binary64 approximation of exponential. The peculiarity of this use case is that the target of the formal verification is not a simple modeling of an external code; it is an actual floating-point function defined in the logic of the Coq proof assistant, which is thus usable inside proofs once its correctness has been fully verified. This function presents all the attributes of a state-of-the-art implementation: bit-level manipulations, large tables of constants, obscure floating-point transformations, exceptional values, etc. This function has been integrated into the proof strategies of the CoqInterval library, bringing a 20× speedup with respect to the previous implementation.
Cite as

Florian Faissole, Paul Geneau de Lamarlière, and Guillaume Melquiond. End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{faissole_et_al:LIPIcs.ITP.2024.14,
  author =	{Faissole, Florian and Geneau de Lamarli\`{e}re, Paul and Melquiond, Guillaume},
  title =	{{End-To-End Formal Verification of a Fast and Accurate Floating-Point Approximation}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.14},
  URN =		{urn:nbn:de:0030-drops-207420},
  doi =		{10.4230/LIPIcs.ITP.2024.14},
  annote =	{Keywords: Program verification, floating-point arithmetic, formal proof, automated reasoning, mathematical library}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.35
Formal Verification of the Empty Hexagon Number

Authors: Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
A recent breakthrough in computer-assisted mathematics showed that every set of 30 points in the plane in general position (i.e., no three points on a common line) contains an empty convex hexagon. Heule and Scheucher solved this problem with a combination of geometric insights and automated reasoning techniques by constructing CNF formulas ϕ_n, with O(n⁴) clauses, such that if ϕ_n is unsatisfiable then every set of n points in general position must contain an empty convex hexagon. An unsatisfiability proof for n = 30 was then found with a SAT solver using 17 300 CPU hours of parallel computation. In this paper, we formalize and verify this result in the Lean theorem prover. Our formalization covers ideas in discrete computational geometry and SAT encoding techniques by introducing a framework that connects geometric objects to propositional assignments. We see this as a key step towards the formal verification of other SAT-based results in geometry, since the abstractions we use have been successfully applied to similar problems. Overall, we hope that our work sets a new standard for the verification of geometry problems relying on extensive computation, and that it increases the trust the mathematical community places in computer-assisted proofs.
Cite as

Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule. Formal Verification of the Empty Hexagon Number. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{subercaseaux_et_al:LIPIcs.ITP.2024.35,
  author =	{Subercaseaux, Bernardo and Nawrocki, Wojciech and Gallicchio, James and Codel, Cayden and Carneiro, Mario and Heule, Marijn J. H.},
  title =	{{Formal Verification of the Empty Hexagon Number}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.35},
  URN =		{urn:nbn:de:0030-drops-207633},
  doi =		{10.4230/LIPIcs.ITP.2024.35},
  annote =	{Keywords: Empty Hexagon Number, Discrete Computational Geometry, Erd\H{o}s-Szekeres}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.23
AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction

Authors: Adam Cicherski, Anna Lisiecka, and Norbert Dojer

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
The success of pangenome-based approaches to genomics analysis depends largely on the existence of efficient methods for constructing pangenome graphs that are applicable to large genome collections. In the current paper we present AlfaPang, a new pangenome graph building algorithm. AlfaPang is based on a novel alignment-free approach that allows to construct pangenome graphs using significantly less computational resources than state-of-the-art tools. The code of AlfaPang is freely available at https://github.com/AdamCicherski/AlfaPang.
Cite as

Adam Cicherski, Anna Lisiecka, and Norbert Dojer. AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cicherski_et_al:LIPIcs.WABI.2024.23,
  author =	{Cicherski, Adam and Lisiecka, Anna and Dojer, Norbert},
  title =	{{AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.23},
  URN =		{urn:nbn:de:0030-drops-206673},
  doi =		{10.4230/LIPIcs.WABI.2024.23},
  annote =	{Keywords: pangenome, variation graph, genome alignment, population genomics}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.8
Applying the Safe-And-Complete Framework to Practical Genome Assembly

Authors: Sebastian Schmidt, Santeri Toivonen, Paul Medvedev, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Despite the long history of genome assembly research, there remains a large gap between the theoretical and practical work. There is practical software with little theoretical underpinning of accuracy on one hand and theoretical algorithms which have not been adopted in practice on the other. In this paper we attempt to bridge the gap between theory and practice by showing how the theoretical safe-and-complete framework can be integrated into existing assemblers in order to improve contiguity. The optimal algorithm in this framework, called the omnitig algorithm, has not been used in practice due to its complexity and its lack of robustness to real data. Instead, we pursue a simplified notion of omnitigs (simple omnitigs), giving an efficient algorithm to compute them and demonstrating their safety under certain conditions. We modify two assemblers (wtdbg2 and Flye) by replacing their unitig algorithm with the simple omnitig algorithm. We test our modifications using real HiFi data from the D. melanogaster and the C. elegans genomes. Our modified algorithms lead to a substantial improvement in alignment-based contiguity, with negligible additional computational costs and either no or a small increase in the number of misassemblies.
Cite as

Sebastian Schmidt, Santeri Toivonen, Paul Medvedev, and Alexandru I. Tomescu. Applying the Safe-And-Complete Framework to Practical Genome Assembly. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schmidt_et_al:LIPIcs.WABI.2024.8,
  author =	{Schmidt, Sebastian and Toivonen, Santeri and Medvedev, Paul and Tomescu, Alexandru I.},
  title =	{{Applying the Safe-And-Complete Framework to Practical Genome Assembly}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.8},
  URN =		{urn:nbn:de:0030-drops-206520},
  doi =		{10.4230/LIPIcs.WABI.2024.8},
  annote =	{Keywords: Genome assembly, Omnitigs, Safe-and-complete framework, graph algorithm, HiFi sequencing data, Assembly evaluation}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.15
Antichain with SAT and Tries

Authors: Lukáš Holík and Pavol Vargovčík

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

Abstract
We introduce a SAT-enabled version of an antichain algorithm for checking language emptiness of alternating finite automata (AFA) with complex transition relations encoded as compact logical formulae. The SAT solver is used to compute predecessors of AFA configurations, and at the same time, to evaluate the subsumption of newly found configurations in the antichain of the previously found ones. The algorithm could be naively implemented by an incremental SAT solver where the growing antichain is represented by adding new clauses. To make it efficient, we 1) force the SAT solver to prioritize largest/subsumption-strongest predecessors (so that weaker configurations are not even generated), and 2) store the antichain clauses in a special variant of a trie that allows fast subsumption testing. The experimental results suggest that the resulting emptiness checker is very efficient compared to the state of the art and that our techniques improve the performance of the SAT solver.
Cite as

Lukáš Holík and Pavol Vargovčík. Antichain with SAT and Tries. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{holik_et_al:LIPIcs.SAT.2024.15,
  author =	{Hol{\'\i}k, Luk\'{a}\v{s} and Vargov\v{c}{\'\i}k, Pavol},
  title =	{{Antichain with SAT and Tries}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{15:1--15:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.15},
  URN =		{urn:nbn:de:0030-drops-205372},
  doi =		{10.4230/LIPIcs.SAT.2024.15},
  annote =	{Keywords: SAT, Trie, Antichain, Alternating automata, Subset query}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.5
The Flower Calculus

Authors: Pablo Donato

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce’s existential graphs. It works as a rewriting system over inductive objects called "flowers", that enjoy both a graphical interpretation as topological diagrams, and a textual presentation as nested sequents akin to coherent formulas. Importantly, the calculus dispenses completely with the traditional notion of symbolic connective, operating solely on nested flowers containing atomic predicates. We prove both the soundness of the full calculus and the completeness of an analytic fragment with respect to Kripke semantics. This provides to our knowledge the first analyticity result for a proof system based on existential graphs, adapting semantic cut-elimination techniques to a deep inference setting. Furthermore, the kernel of rules targetted by completeness is fully invertible, a desirable property for both automated and interactive proof search.
Cite as

Pablo Donato. The Flower Calculus. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{donato:LIPIcs.FSCD.2024.5,
  author =	{Donato, Pablo},
  title =	{{The Flower Calculus}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.5},
  URN =		{urn:nbn:de:0030-drops-203343},
  doi =		{10.4230/LIPIcs.FSCD.2024.5},
  annote =	{Keywords: deep inference, graphical calculi, existential graphs, intuitionistic logic, Kripke semantics, cut-elimination}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2024.51
Efficient Algorithms for Complexes of Persistence Modules with Applications

Authors: Tamal K. Dey, Florian Russold, and Shreyas N. Samaga

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and develop an efficient algorithm to compute the homology of a complex of presentations. To deal with inputs that are not given in terms of presentations, we give an efficient algorithm to compute a presentation of a morphism of persistence modules. This allows us to compute persistent (co)homology of instances giving rise to complexes of non-free modules. Our methods lead to a new efficient algorithm for computing the persistent homology of simplicial towers and they enable efficient algorithms to compute the persistent homology of cosheaves over simplicial towers and cohomology of persistent sheaves on simplicial complexes. We also show that we can compute the cohomology of persistent sheaves over arbitrary finite posets by reducing the computation to a computation over simplicial complexes.
Cite as

Tamal K. Dey, Florian Russold, and Shreyas N. Samaga. Efficient Algorithms for Complexes of Persistence Modules with Applications. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dey_et_al:LIPIcs.SoCG.2024.51,
  author =	{Dey, Tamal K. and Russold, Florian and Samaga, Shreyas N.},
  title =	{{Efficient Algorithms for Complexes of Persistence Modules with Applications}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.51},
  URN =		{urn:nbn:de:0030-drops-199969},
  doi =		{10.4230/LIPIcs.SoCG.2024.51},
  annote =	{Keywords: Persistent (co)homology, Persistence modules, Sheaves, Presentations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.32
Isometric Path Complexity of Graphs

Authors: Dibyayan Chakraborty, Jérémie Chalopin, Florent Foucaud, and Yann Vaxès

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
A set S of isometric paths of a graph G is "v-rooted", where v is a vertex of G, if v is one of the end-vertices of all the isometric paths in S. The isometric path complexity of a graph G, denoted by ipco (G), is the minimum integer k such that there exists a vertex v ∈ V(G) satisfying the following property: the vertices of any isometric path P of G can be covered by k many v-rooted isometric paths. First, we provide an O(n² m)-time algorithm to compute the isometric path complexity of a graph with n vertices and m edges. Then we show that the isometric path complexity remains bounded for graphs in three seemingly unrelated graph classes, namely, hyperbolic graphs, (theta, prism, pyramid)-free graphs, and outerstring graphs. Hyperbolic graphs are extensively studied in Metric Graph Theory. The class of (theta, prism, pyramid)-free graphs are extensively studied in Structural Graph Theory, e.g. in the context of the Strong Perfect Graph Theorem. The class of outerstring graphs is studied in Geometric Graph Theory and Computational Geometry. Our results also show that the distance functions of these (structurally) different graph classes are more similar than previously thought. There is a direct algorithmic consequence of having small isometric path complexity. Specifically, using a result of Chakraborty et al. [ISAAC 2022], we show that if the isometric path complexity of a graph G is bounded by a constant k, then there exists a k-factor approximation algorithm for Isometric Path Cover, whose objective is to cover all vertices of a graph with a minimum number of isometric paths.
Cite as

Dibyayan Chakraborty, Jérémie Chalopin, Florent Foucaud, and Yann Vaxès. Isometric Path Complexity of Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2023.32,
  author =	{Chakraborty, Dibyayan and Chalopin, J\'{e}r\'{e}mie and Foucaud, Florent and Vax\`{e}s, Yann},
  title =	{{Isometric Path Complexity of Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.32},
  URN =		{urn:nbn:de:0030-drops-185666},
  doi =		{10.4230/LIPIcs.MFCS.2023.32},
  annote =	{Keywords: Shortest paths, Isometric path complexity, Hyperbolic graphs, Truemper Configurations, Outerstring graphs, Isometric Path Cover}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.42
Recontamination Helps a Lot to Hunt a Rabbit

Authors: Thomas Dissaux, Foivos Fioravantes, Harmender Gahlawat, and Nicolas Nisse

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if it is not shot, must move to a neighbouring vertex after each round. The Rabbit player wins if it can ensure that its position is never shot. The Hunter player wins otherwise. The hunter number h(G) of a graph G is the minimum integer k such that the Hunter player has a winning strategy (i.e., allowing him to win whatever be the strategy of the Rabbit player). This game has been studied in several graph classes, in particular in bipartite graphs (grids, trees, hypercubes...), but the computational complexity of computing h(G) remains open in general graphs and even in more restricted graph classes such as trees. To progress further in this study, we propose a notion of monotonicity (a well-studied and useful property in classical pursuit-evasion games such as Graph Searching games) for the Hunters and Rabbit game imposing that, roughly, a vertex that has already been shot "must not host the rabbit anymore". This allows us to obtain new results in various graph classes. More precisely, let the monotone hunter number mh(G) of a graph G be the minimum integer k such that the Hunter player has a monotone winning strategy. We show that pw(G) ≤ mh(G) ≤ pw(G)+1 for any graph G with pathwidth pw(G), which implies that computing mh(G), or even approximating mh(G) up to an additive constant, is NP-hard. Then, we show that mh(G) can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which allow us to relate the monotone hunter number with the pathwidth in some of these graph classes. In all cases, this allows us to specify the hunter number or to show that there may be an arbitrary gap between h and mh, i.e., that monotonicity does not help. In particular, we show that, for every k ≥ 3, there exists a tree T with h(T) = 2 and mh(T) = k. We conclude by proving that computing h (resp., mh) is FPT parameterised by the minimum size of a vertex cover.
Cite as

Thomas Dissaux, Foivos Fioravantes, Harmender Gahlawat, and Nicolas Nisse. Recontamination Helps a Lot to Hunt a Rabbit. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dissaux_et_al:LIPIcs.MFCS.2023.42,
  author =	{Dissaux, Thomas and Fioravantes, Foivos and Gahlawat, Harmender and Nisse, Nicolas},
  title =	{{Recontamination Helps a Lot to Hunt a Rabbit}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.42},
  URN =		{urn:nbn:de:0030-drops-185763},
  doi =		{10.4230/LIPIcs.MFCS.2023.42},
  annote =	{Keywords: Hunter and Rabbit, Monotonicity, Graph Searching}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.88
Checking Presence Reachability Properties on Parameterized Shared-Memory Systems

Authors: Nicolas Waldburger

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the standard model with finitely many registers, we tackle round-based shared-memory systems with fresh registers at each round. In the latter model, both the number of processes and the number of registers are unbounded, making verification particularly challenging. The properties studied are generic presence reachability objectives, which subsume classical questions such as safety or synchronization by expressing the presence or absence of processes in some states. In the more general round-based setting, we establish that the parameterized verification of presence reachability properties is PSPACE-complete. Moreover, for the roundless model with finitely many registers, we prove that the complexity drops down to NP-complete and we provide several natural restrictions that make the problem solvable in polynomial time.
Cite as

Nicolas Waldburger. Checking Presence Reachability Properties on Parameterized Shared-Memory Systems. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 88:1-88:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{waldburger:LIPIcs.MFCS.2023.88,
  author =	{Waldburger, Nicolas},
  title =	{{Checking Presence Reachability Properties on Parameterized Shared-Memory Systems}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{88:1--88:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.88},
  URN =		{urn:nbn:de:0030-drops-186225},
  doi =		{10.4230/LIPIcs.MFCS.2023.88},
  annote =	{Keywords: Verification, Parameterized models, Distributed algorithms}
}
Document
DOI: 10.4230/LIPIcs.SAND.2023.7
When Should You Wait Before Updating? - Toward a Robustness Refinement

Authors: Swan Dubois, Laurent Feuilloley, Franck Petit, and Mikaël Rabie

Published in: LIPIcs, Volume 257, 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)

Abstract
Consider a dynamic network and a given distributed problem. At any point in time, there might exist several solutions that are equally good with respect to the problem specification, but that are different from an algorithmic perspective, because some could be easier to update than others when the network changes. In other words, one would prefer to have a solution that is more robust to topological changes in the network; and in this direction the best scenario would be that the solution remains correct despite the dynamic of the network. In [Arnaud Casteigts et al., 2020], the authors introduced a very strong robustness criterion: they required that for any removal of edges that maintain the network connected, the solution remains valid. They focus on the maximal independent set problem, and their approach consists in characterizing the graphs in which there exists a robust solution (the existential problem), or even stronger, where any solution is robust (the universal problem). As the robustness criteria is very demanding, few graphs have a robust solution, and even fewer are such that all of their solutions are robust. In this paper, we ask the following question: Can we have robustness for a larger class of networks, if we bound the number k of edge removals allowed? To answer this question, we consider three classic problems: maximal independent set, minimal dominating set and maximal matching. For the universal problem, the answers for the three cases are surprisingly different. For minimal dominating set, the class does not depend on the number of edges removed. For maximal matching, removing only one edge defines a robust class related to perfect matchings, but for all other bounds k, the class is the same as for an arbitrary number of edge removals. Finally, for maximal independent set, there is a strict hierarchy of classes: the class for the bound k is strictly larger than the class for bound k+1. For the robustness notion of [Arnaud Casteigts et al., 2020], no characterization of the class for the existential problem is known, only a polynomial-time recognition algorithm. We show that the situation is even worse for bounded k: even for k = 1, it is NP-hard to decide whether a graph has a robust maximal independent set.
Cite as

Swan Dubois, Laurent Feuilloley, Franck Petit, and Mikaël Rabie. When Should You Wait Before Updating? - Toward a Robustness Refinement. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dubois_et_al:LIPIcs.SAND.2023.7,
  author =	{Dubois, Swan and Feuilloley, Laurent and Petit, Franck and Rabie, Mika\"{e}l},
  title =	{{When Should You Wait Before Updating? - Toward a Robustness Refinement}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2023.7},
  URN =		{urn:nbn:de:0030-drops-179435},
  doi =		{10.4230/LIPIcs.SAND.2023.7},
  annote =	{Keywords: Robustness, dynamic network, temporal graphs, edge removal, connectivity, footprint, packing/covering problems, maximal independent set, maximal matching, minimum dominating set, perfect matching, NP-hardness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.104
Threshold Rates of Code Ensembles: Linear Is Best

Authors: Nicolas Resch and Chen Yuan

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
In this work, we prove new results concerning the combinatorial properties of random linear codes. By applying the thresholds framework from Mosheiff et al. (FOCS 2020) we derive fine-grained results concerning the list-decodability and -recoverability of random linear codes. Firstly, we prove a lower bound on the list-size required for random linear codes over 𝔽_q ε-close to capacity to list-recover with error radius ρ and input lists of size 𝓁. We show that the list-size L must be at least {log_q binom{q,𝓁}}-R}/ε, where R is the rate of the random linear code. This is analogous to a lower bound for list-decoding that was recently obtained by Guruswami et al. (IEEE TIT 2021B). As a comparison, we also pin down the list size of random codes which is {log_q binom{q,𝓁}}/ε. This result almost closes the O({q log L}/L) gap left by Guruswami et al. (IEEE TIT 2021A). This leaves open the possibility (that we consider likely) that random linear codes perform better than the random codes for list-recoverability, which is in contrast to a recent gap shown for the case of list-recovery from erasures (Guruswami et al., IEEE TIT 2021B). Next, we consider list-decoding with constant list-sizes. Specifically, we obtain new lower bounds on the rate required for: - List-of-3 decodability of random linear codes over 𝔽₂; - List-of-2 decodability of random linear codes over 𝔽_q (for any q). This expands upon Guruswami et al. (IEEE TIT 2021A) which only studied list-of-2 decodability of random linear codes over 𝔽₂. Further, in both cases we are able to show that the rate is larger than that which is possible for uniformly random codes. A conclusion that we draw from our work is that, for many combinatorial properties of interest, random linear codes actually perform better than uniformly random codes, in contrast to the apparently standard intuition that uniformly random codes are best.
Cite as

Nicolas Resch and Chen Yuan. Threshold Rates of Code Ensembles: Linear Is Best. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 104:1-104:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{resch_et_al:LIPIcs.ICALP.2022.104,
  author =	{Resch, Nicolas and Yuan, Chen},
  title =	{{Threshold Rates of Code Ensembles: Linear Is Best}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{104:1--104:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.104},
  URN =		{urn:nbn:de:0030-drops-164456},
  doi =		{10.4230/LIPIcs.ICALP.2022.104},
  annote =	{Keywords: Random Linear Codes, List-Decoding, List-Recovery, Threshold Rates}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.113
Parameterized Safety Verification of Round-Based Shared-Memory Systems

Authors: Nathalie Bertrand, Nicolas Markey, Ocan Sankur, and Nicolas Waldburger

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm [James Aspnes, 2002], we consider round-based distributed algorithms communicating with shared memory. A particular challenge in these systems is that 1) the number of processes is unbounded, and, more importantly, 2) there is a fresh set of registers at each round. A verification algorithm thus needs to manage both sources of infinity. In this setting, we prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For negative instances of the safety verification problem, we also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered.
Cite as

Nathalie Bertrand, Nicolas Markey, Ocan Sankur, and Nicolas Waldburger. Parameterized Safety Verification of Round-Based Shared-Memory Systems. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 113:1-113:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bertrand_et_al:LIPIcs.ICALP.2022.113,
  author =	{Bertrand, Nathalie and Markey, Nicolas and Sankur, Ocan and Waldburger, Nicolas},
  title =	{{Parameterized Safety Verification of Round-Based Shared-Memory Systems}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{113:1--113:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.113},
  URN =		{urn:nbn:de:0030-drops-164541},
  doi =		{10.4230/LIPIcs.ICALP.2022.113},
  annote =	{Keywords: Verification, Parameterized models, Distributed algorithms}
}
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