Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Amir Abboud and Nathan Wallheimer. Worst-Case to Expander-Case Reductions: Derandomized and Generalized. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{abboud_et_al:LIPIcs.ESA.2024.4, author = {Abboud, Amir and Wallheimer, Nathan}, title = {{Worst-Case to Expander-Case Reductions: Derandomized and Generalized}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {4:1--4:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.4}, URN = {urn:nbn:de:0030-drops-210751}, doi = {10.4230/LIPIcs.ESA.2024.4}, annote = {Keywords: Fine-grained complexity, expander graphs, self-reductions, worst-case to expander-case, expander decomposition, dynamic algorithms, exact and parameterized complexity, max-cut, maximum matching, k-clique detection, densest subgraph} }
Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Chandra Chekuri and Rhea Jain. Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.41, author = {Chekuri, Chandra and Jain, Rhea}, title = {{Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {41:1--41:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.41}, URN = {urn:nbn:de:0030-drops-211124}, doi = {10.4230/LIPIcs.ESA.2024.41}, annote = {Keywords: Buy-at-bulk, Hop-constrained network design, LP integrality gap, Fault-tolerant network design} }
Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Chandra Chekuri, Rhea Jain, Shubhang Kulkarni, Da Wei Zheng, and Weihao Zhu. From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.42, author = {Chekuri, Chandra and Jain, Rhea and Kulkarni, Shubhang and Zheng, Da Wei and Zhu, Weihao}, title = {{From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {42:1--42:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.42}, URN = {urn:nbn:de:0030-drops-211134}, doi = {10.4230/LIPIcs.ESA.2024.42}, annote = {Keywords: Directed Planar Graphs, Submodular Functions, Steiner Tree, Network Design} }
Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Lars Gottesbüren, Nikos Parotsidis, and Maximilian Probst Gutenberg. Practical Expander Decomposition. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 61:1-61:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{gottesburen_et_al:LIPIcs.ESA.2024.61, author = {Gottesb\"{u}ren, Lars and Parotsidis, Nikos and Gutenberg, Maximilian Probst}, title = {{Practical Expander Decomposition}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {61:1--61:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.61}, URN = {urn:nbn:de:0030-drops-211323}, doi = {10.4230/LIPIcs.ESA.2024.61}, annote = {Keywords: Expander Decomposition, Clustering, Graph Algorithms} }
Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Rajmohan Rajaraman and Omer Wasim. Competitive Capacitated Online Recoloring. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{rajaraman_et_al:LIPIcs.ESA.2024.95, author = {Rajaraman, Rajmohan and Wasim, Omer}, title = {{Competitive Capacitated Online Recoloring}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {95:1--95:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-338-6}, ISSN = {1868-8969}, year = {2024}, volume = {308}, editor = {Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.95}, URN = {urn:nbn:de:0030-drops-211666}, doi = {10.4230/LIPIcs.ESA.2024.95}, annote = {Keywords: online algorithms, competitive ratio, recoloring, resource augmentation} }
Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Yaron Fairstein, Joseph (Seffi) Naor, and Tomer Tsachor. Distributional Online Weighted Paging with Limited Horizon. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{fairstein_et_al:LIPIcs.APPROX/RANDOM.2024.15, author = {Fairstein, Yaron and Naor, Joseph (Seffi) and Tsachor, Tomer}, title = {{Distributional Online Weighted Paging with Limited Horizon}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {15:1--15:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-348-5}, ISSN = {1868-8969}, year = {2024}, volume = {317}, editor = {Kumar, Amit and Ron-Zewi, Noga}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.15}, URN = {urn:nbn:de:0030-drops-210088}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.15}, annote = {Keywords: Online algorithms, Caching, Stochastic analysis, Predictions} }
Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)
Zeta Avarikioti, Stefan Schmid, and Samarth Tiwari. Musketeer: Incentive-Compatible Rebalancing for Payment Channel Networks. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{avarikioti_et_al:LIPIcs.AFT.2024.13, author = {Avarikioti, Zeta and Schmid, Stefan and Tiwari, Samarth}, title = {{Musketeer: Incentive-Compatible Rebalancing for Payment Channel Networks}}, booktitle = {6th Conference on Advances in Financial Technologies (AFT 2024)}, pages = {13:1--13:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-345-4}, ISSN = {1868-8969}, year = {2024}, volume = {316}, editor = {B\"{o}hme, Rainer and Kiffer, Lucianna}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.13}, URN = {urn:nbn:de:0030-drops-209494}, doi = {10.4230/LIPIcs.AFT.2024.13}, annote = {Keywords: Blockchains, Payment Channel Networks, Rebalancing, Game Theory} }
Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
Václav Blažej, Dušan Knop, Jan Pokorný, and Šimon Schierreich. Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{blazej_et_al:LIPIcs.MFCS.2024.29, author = {Bla\v{z}ej, V\'{a}clav and Knop, Du\v{s}an and Pokorn\'{y}, Jan and Schierreich, \v{S}imon}, title = {{Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {29:1--29:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.29}, URN = {urn:nbn:de:0030-drops-205857}, doi = {10.4230/LIPIcs.MFCS.2024.29}, annote = {Keywords: Equitable Connected Partition, structural parameters, fixed-parameter tractability, N-fold integer programming, tree-width, shrub-depth, modular-width} }
Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
Syamantak Das, Nikhil Kumar, and Daniel Vaz. Nearly-Tight Bounds for Flow Sparsifiers in Quasi-Bipartite Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{das_et_al:LIPIcs.MFCS.2024.45, author = {Das, Syamantak and Kumar, Nikhil and Vaz, Daniel}, title = {{Nearly-Tight Bounds for Flow Sparsifiers in Quasi-Bipartite Graphs}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {45:1--45:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-335-5}, ISSN = {1868-8969}, year = {2024}, volume = {306}, editor = {Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.45}, URN = {urn:nbn:de:0030-drops-206018}, doi = {10.4230/LIPIcs.MFCS.2024.45}, annote = {Keywords: Graph Sparsification, Cut Sparsifiers, Flow Sparsifiers, Quasi-bipartite Graphs, Bounded Treewidth} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yu Chen, Michael Kapralov, Mikhail Makarov, and Davide Mazzali. On the Streaming Complexity of Expander Decomposition. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{chen_et_al:LIPIcs.ICALP.2024.46, author = {Chen, Yu and Kapralov, Michael and Makarov, Mikhail and Mazzali, Davide}, title = {{On the Streaming Complexity of Expander Decomposition}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {46:1--46:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.46}, URN = {urn:nbn:de:0030-drops-201890}, doi = {10.4230/LIPIcs.ICALP.2024.46}, annote = {Keywords: Graph Sketching, Dynamic Streaming, Expander Decomposition} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Ilan Doron-Arad and Joseph (Seffi) Naor. Non-Linear Paging. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{doronarad_et_al:LIPIcs.ICALP.2024.57, author = {Doron-Arad, Ilan and Naor, Joseph (Seffi)}, title = {{Non-Linear Paging}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {57:1--57:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.57}, URN = {urn:nbn:de:0030-drops-202000}, doi = {10.4230/LIPIcs.ICALP.2024.57}, annote = {Keywords: paging, competitive analysis, non-linear paging, submodular and supermodular functions} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva. Optimal Electrical Oblivious Routing on Expanders. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{florescu_et_al:LIPIcs.ICALP.2024.65, author = {Florescu, Cella and Kyng, Rasmus and Gutenberg, Maximilian Probst and Sachdeva, Sushant}, title = {{Optimal Electrical Oblivious Routing on Expanders}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {65:1--65:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.65}, URN = {urn:nbn:de:0030-drops-202083}, doi = {10.4230/LIPIcs.ICALP.2024.65}, annote = {Keywords: Expanders, Oblivious routing for 𝓁\underlinep, Electrical flow routing} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Adam Karczmarz and Marcin Smulewicz. Fully Dynamic Strongly Connected Components in Planar Digraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{karczmarz_et_al:LIPIcs.ICALP.2024.95, author = {Karczmarz, Adam and Smulewicz, Marcin}, title = {{Fully Dynamic Strongly Connected Components in Planar Digraphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {95:1--95:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.95}, URN = {urn:nbn:de:0030-drops-202388}, doi = {10.4230/LIPIcs.ICALP.2024.95}, annote = {Keywords: dynamic strongly connected components, dynamic strong connectivity, dynamic reachability, planar graphs} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120, author = {Sadeh, Yaniv and Kaplan, Haim}, title = {{Caching Connections in Matchings}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {120:1--120:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.120}, URN = {urn:nbn:de:0030-drops-202639}, doi = {10.4230/LIPIcs.ICALP.2024.120}, annote = {Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms} }
Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)
Gramoz Goranci, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan. Electrical Flows for Polylogarithmic Competitive Oblivious Routing. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 55:1-55:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{goranci_et_al:LIPIcs.ITCS.2024.55, author = {Goranci, Gramoz and Henzinger, Monika and R\"{a}cke, Harald and Sachdeva, Sushant and Sricharan, A. R.}, title = {{Electrical Flows for Polylogarithmic Competitive Oblivious Routing}}, booktitle = {15th Innovations in Theoretical Computer Science Conference (ITCS 2024)}, pages = {55:1--55:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-309-6}, ISSN = {1868-8969}, year = {2024}, volume = {287}, editor = {Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.55}, URN = {urn:nbn:de:0030-drops-195830}, doi = {10.4230/LIPIcs.ITCS.2024.55}, annote = {Keywords: oblivious routing, electrical flows} }
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