Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Mikkel Abrahamsen, Linda Kleist, and Tillmann Miltzow. Geometric Embeddability of Complexes Is ∃ℝ-Complete. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2023.1, author = {Abrahamsen, Mikkel and Kleist, Linda and Miltzow, Tillmann}, title = {{Geometric Embeddability of Complexes Is \exists\mathbb{R}-Complete}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {1:1--1:19}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.1}, URN = {urn:nbn:de:0030-drops-178518}, doi = {10.4230/LIPIcs.SoCG.2023.1}, annote = {Keywords: simplicial complex, geometric embedding, linear embedding, hypergraph, recognition, existential theory of the reals} }
Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Jack Stade and Jamie Tucker-Foltz. Topological Universality of the Art Gallery Problem. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 58:1-58:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{stade_et_al:LIPIcs.SoCG.2023.58, author = {Stade, Jack and Tucker-Foltz, Jamie}, title = {{Topological Universality of the Art Gallery Problem}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {58:1--58:13}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.58}, URN = {urn:nbn:de:0030-drops-179082}, doi = {10.4230/LIPIcs.SoCG.2023.58}, annote = {Keywords: Art gallery, Homeomorphism, Exists-R, ETR, Semi-algebraic sets, Universality} }
Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)
Paul Jungeblut, Linda Kleist, and Tillmann Miltzow. The Complexity of the Hausdorff Distance. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{jungeblut_et_al:LIPIcs.SoCG.2022.48, author = {Jungeblut, Paul and Kleist, Linda and Miltzow, Tillmann}, title = {{The Complexity of the Hausdorff Distance}}, booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)}, pages = {48:1--48:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-227-3}, ISSN = {1868-8969}, year = {2022}, volume = {224}, editor = {Goaoc, Xavier and Kerber, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.48}, URN = {urn:nbn:de:0030-drops-160567}, doi = {10.4230/LIPIcs.SoCG.2022.48}, annote = {Keywords: Hausdorff Distance, Semi-Algebraic Set, Existential Theory of the Reals, Universal Existential Theory of the Reals, Complexity Theory} }
Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)
Anders Aamand, Mikkel Abrahamsen, Jakob Bæk Tejs Knudsen, and Peter Michael Reichstein Rasmussen. Classifying Convex Bodies by Their Contact and Intersection Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{aamand_et_al:LIPIcs.SoCG.2021.3, author = {Aamand, Anders and Abrahamsen, Mikkel and Knudsen, Jakob B{\ae}k Tejs and Rasmussen, Peter Michael Reichstein}, title = {{Classifying Convex Bodies by Their Contact and Intersection Graphs}}, booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)}, pages = {3:1--3:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-184-9}, ISSN = {1868-8969}, year = {2021}, volume = {189}, editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.3}, URN = {urn:nbn:de:0030-drops-138024}, doi = {10.4230/LIPIcs.SoCG.2021.3}, annote = {Keywords: convex body, contact graph, intersection graph} }
Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)
Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta. Chasing Puppies: Mobile Beacon Routing on Closed Curves. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2021.5, author = {Abrahamsen, Mikkel and Erickson, Jeff and Kostitsyna, Irina and L\"{o}ffler, Maarten and Miltzow, Tillmann and Urhausen, J\'{e}r\^{o}me and Vermeulen, Jordi and Viglietta, Giovanni}, title = {{Chasing Puppies: Mobile Beacon Routing on Closed Curves}}, booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)}, pages = {5:1--5:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-184-9}, ISSN = {1868-8969}, year = {2021}, volume = {189}, editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.5}, URN = {urn:nbn:de:0030-drops-138046}, doi = {10.4230/LIPIcs.SoCG.2021.5}, annote = {Keywords: Beacon routing, navigation, generic smooth curves, puppies} }
Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)
Simon B. Hengeveld and Tillmann Miltzow. A Practical Algorithm with Performance Guarantees for the Art Gallery Problem. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 44:1-44:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{hengeveld_et_al:LIPIcs.SoCG.2021.44, author = {Hengeveld, Simon B. and Miltzow, Tillmann}, title = {{A Practical Algorithm with Performance Guarantees for the Art Gallery Problem}}, booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)}, pages = {44:1--44:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-184-9}, ISSN = {1868-8969}, year = {2021}, volume = {189}, editor = {Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.44}, URN = {urn:nbn:de:0030-drops-138433}, doi = {10.4230/LIPIcs.SoCG.2021.44}, annote = {Keywords: Art Gallery, Parametrized complexity, Integer Programming, Visibility} }
Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Marc van Kreveld, Tillmann Miltzow, Tim Ophelders, Willem Sonke, and Jordi L. Vermeulen. Between Shapes, Using the Hausdorff Distance. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{vankreveld_et_al:LIPIcs.ISAAC.2020.13, author = {van Kreveld, Marc and Miltzow, Tillmann and Ophelders, Tim and Sonke, Willem and Vermeulen, Jordi L.}, title = {{Between Shapes, Using the Hausdorff Distance}}, booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)}, pages = {13:1--13:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-173-3}, ISSN = {1868-8969}, year = {2020}, volume = {181}, editor = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.13}, URN = {urn:nbn:de:0030-drops-133572}, doi = {10.4230/LIPIcs.ISAAC.2020.13}, annote = {Keywords: computational geometry, Hausdorff distance, shape interpolation} }
Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Édouard Bonnet, Nicolas Grelier, and Tillmann Miltzow. Maximum Clique in Disk-Like Intersection Graphs. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{bonnet_et_al:LIPIcs.FSTTCS.2020.17, author = {Bonnet, \'{E}douard and Grelier, Nicolas and Miltzow, Tillmann}, title = {{Maximum Clique in Disk-Like Intersection Graphs}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {17:1--17:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.17}, URN = {urn:nbn:de:0030-drops-132587}, doi = {10.4230/LIPIcs.FSTTCS.2020.17}, annote = {Keywords: Disk Graphs, Intersection Graphs, Maximum Clique, Algorithms, NP-hardness, APX-hardness} }
Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)
Tillmann Miltzow, Irene Parada, Willem Sonke, Bettina Speckmann, and Jules Wulms. Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 78:1-78:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{miltzow_et_al:LIPIcs.SoCG.2020.78, author = {Miltzow, Tillmann and Parada, Irene and Sonke, Willem and Speckmann, Bettina and Wulms, Jules}, title = {{Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy}}, booktitle = {36th International Symposium on Computational Geometry (SoCG 2020)}, pages = {78:1--78:5}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-143-6}, ISSN = {1868-8969}, year = {2020}, volume = {164}, editor = {Cabello, Sergio and Chen, Danny Z.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.78}, URN = {urn:nbn:de:0030-drops-122363}, doi = {10.4230/LIPIcs.SoCG.2020.78}, annote = {Keywords: Sliding cubes, Reconfiguration, Modular robots} }
Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Akanksha Agrawal, Arindam Biswas, Édouard Bonnet, Nick Brettell, Radu Curticapean, Dániel Marx, Tillmann Miltzow, Venkatesh Raman, and Saket Saurabh. Parameterized Streaming Algorithms for Min-Ones d-SAT. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{agrawal_et_al:LIPIcs.FSTTCS.2019.8, author = {Agrawal, Akanksha and Biswas, Arindam and Bonnet, \'{E}douard and Brettell, Nick and Curticapean, Radu and Marx, D\'{a}niel and Miltzow, Tillmann and Raman, Venkatesh and Saurabh, Saket}, title = {{Parameterized Streaming Algorithms for Min-Ones d-SAT}}, booktitle = {39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)}, pages = {8:1--8:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-131-3}, ISSN = {1868-8969}, year = {2019}, volume = {150}, editor = {Chattopadhyay, Arkadev and Gastin, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.8}, URN = {urn:nbn:de:0030-drops-115708}, doi = {10.4230/LIPIcs.FSTTCS.2019.8}, annote = {Keywords: min, ones, sat, d-sat, parameterized, kernelization, streaming, space, efficient, algorithm, parameter} }
Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)
Jeff Erickson and Yipu Wang. Topologically Trivial Closed Walks in Directed Surface Graphs. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{erickson_et_al:LIPIcs.SoCG.2019.34, author = {Erickson, Jeff and Wang, Yipu}, title = {{Topologically Trivial Closed Walks in Directed Surface Graphs}}, booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)}, pages = {34:1--34:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-104-7}, ISSN = {1868-8969}, year = {2019}, volume = {129}, editor = {Barequet, Gill and Wang, Yusu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.34}, URN = {urn:nbn:de:0030-drops-104383}, doi = {10.4230/LIPIcs.SoCG.2019.34}, annote = {Keywords: computational topology, surface-embedded graphs, homotopy, homology, strong connectivity, hyperbolic geometry, medial axes, context-free grammars} }
Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)
Mikkel Abrahamsen, Anna Adamaszek, and Tillmann Miltzow. Irrational Guards are Sometimes Needed. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2017.3, author = {Abrahamsen, Mikkel and Adamaszek, Anna and Miltzow, Tillmann}, title = {{Irrational Guards are Sometimes Needed}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {3:1--3:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, editor = {Aronov, Boris and Katz, Matthew J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.3}, URN = {urn:nbn:de:0030-drops-71946}, doi = {10.4230/LIPIcs.SoCG.2017.3}, annote = {Keywords: art gallery problem, computational geometry, irrational numbers} }
Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)
Csaba Biró, Édouard Bonnet, Dániel Marx, Tillmann Miltzow, and Pawel Rzazewski. Fine-Grained Complexity of Coloring Unit Disks and Balls. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{biro_et_al:LIPIcs.SoCG.2017.18, author = {Bir\'{o}, Csaba and Bonnet, \'{E}douard and Marx, D\'{a}niel and Miltzow, Tillmann and Rzazewski, Pawel}, title = {{Fine-Grained Complexity of Coloring Unit Disks and Balls}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {18:1--18:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, editor = {Aronov, Boris and Katz, Matthew J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.18}, URN = {urn:nbn:de:0030-drops-71800}, doi = {10.4230/LIPIcs.SoCG.2017.18}, annote = {Keywords: unit disk graphs, unit ball graphs, coloring, exact algorithm} }
Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)
Édouard Bonnet and Tillmann Miltzow. An Approximation Algorithm for the Art Gallery Problem. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{bonnet_et_al:LIPIcs.SoCG.2017.20, author = {Bonnet, \'{E}douard and Miltzow, Tillmann}, title = {{An Approximation Algorithm for the Art Gallery Problem}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {20:1--20:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, editor = {Aronov, Boris and Katz, Matthew J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.20}, URN = {urn:nbn:de:0030-drops-72150}, doi = {10.4230/LIPIcs.SoCG.2017.20}, annote = {Keywords: computational geometry, art gallery, approximation algorithm} }
Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Édouard Bonnet, Tillmann Miltzow, and Pawel Rzazewski. Complexity of Token Swapping and its Variants. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{bonnet_et_al:LIPIcs.STACS.2017.16, author = {Bonnet, \'{E}douard and Miltzow, Tillmann and Rzazewski, Pawel}, title = {{Complexity of Token Swapping and its Variants}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {16:1--16:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.16}, URN = {urn:nbn:de:0030-drops-70185}, doi = {10.4230/LIPIcs.STACS.2017.16}, annote = {Keywords: token swapping, parameterized complexity, NP-hardness, W\lbrack1\rbrack-hardness} }
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