Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Vikrant Ashvinkumar, Aaron Bernstein, Nairen Cao, Christoph Grunau, Bernhard Haeupler, Yonggang Jiang, Danupon Nanongkai, and Hsin-Hao Su. Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{ashvinkumar_et_al:LIPIcs.ESA.2024.13, author = {Ashvinkumar, Vikrant and Bernstein, Aaron and Cao, Nairen and Grunau, Christoph and Haeupler, Bernhard and Jiang, Yonggang and Nanongkai, Danupon and Su, Hsin-Hao}, title = {{Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {13:1--13:15}, 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.2024.13}, URN = {urn:nbn:de:0030-drops-210849}, doi = {10.4230/LIPIcs.ESA.2024.13}, annote = {Keywords: Parallel algorithm, distributed algorithm, shortest paths} }
Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)
Sally Dong and Guanghao Ye. Faster Min-Cost Flow and Approximate Tree Decomposition on Bounded Treewidth Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{dong_et_al:LIPIcs.ESA.2024.49, author = {Dong, Sally and Ye, Guanghao}, title = {{Faster Min-Cost Flow and Approximate Tree Decomposition on Bounded Treewidth Graphs}}, booktitle = {32nd Annual European Symposium on Algorithms (ESA 2024)}, pages = {49:1--49:14}, 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.2024.49}, URN = {urn:nbn:de:0030-drops-211207}, doi = {10.4230/LIPIcs.ESA.2024.49}, annote = {Keywords: Min-cost flow, tree decomposition, interior point method, bounded treewidth graphs} }
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 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 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Lap Chi Lau and Dante Tjowasi. On the Houdré-Tetali Conjecture About an Isoperimetric Constant of Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{lau_et_al:LIPIcs.APPROX/RANDOM.2024.36, author = {Lau, Lap Chi and Tjowasi, Dante}, title = {{On the Houdr\'{e}-Tetali Conjecture About an Isoperimetric Constant of Graphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {36:1--36:18}, 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.2024.36}, URN = {urn:nbn:de:0030-drops-210295}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.36}, annote = {Keywords: Isoperimetric constant, Markov chains, Cheeger’s inequality} }
Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Holden Lee. Parallelising Glauber Dynamics. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{lee:LIPIcs.APPROX/RANDOM.2024.49, author = {Lee, Holden}, title = {{Parallelising Glauber Dynamics}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {49:1--49:24}, 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.2024.49}, URN = {urn:nbn:de:0030-drops-210424}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.49}, annote = {Keywords: sampling, Ising model, parallel algorithm, Markov chain, Glauber dynamics} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Li Chen and Mingquan Ye. High-Accuracy Multicommodity Flows via Iterative Refinement. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{chen_et_al:LIPIcs.ICALP.2024.45, author = {Chen, Li and Ye, Mingquan}, title = {{High-Accuracy Multicommodity Flows via Iterative Refinement}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {45:1--45:19}, 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.2024.45}, URN = {urn:nbn:de:0030-drops-201887}, doi = {10.4230/LIPIcs.ICALP.2024.45}, annote = {Keywords: High-accuracy multicommodity flow, Iterative refinement framework, Convex flow solver} }
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)
Greg Bodwin, Chengyuan Deng, Jie Gao, Gary Hoppenworth, Jalaj Upadhyay, and Chen Wang. The Discrepancy of Shortest Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{bodwin_et_al:LIPIcs.ICALP.2024.27, author = {Bodwin, Greg and Deng, Chengyuan and Gao, Jie and Hoppenworth, Gary and Upadhyay, Jalaj and Wang, Chen}, title = {{The Discrepancy of Shortest Paths}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {27:1--27:20}, 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.2024.27}, URN = {urn:nbn:de:0030-drops-201705}, doi = {10.4230/LIPIcs.ICALP.2024.27}, annote = {Keywords: Discrepancy, hereditary discrepancy, shortest paths, differential privacy} }
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)
Ce Jin, Michael Kapralov, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Connectivity Augmentation. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 93:1-93:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{jin_et_al:LIPIcs.ICALP.2024.93, author = {Jin, Ce and Kapralov, Michael and Mahabadi, Sepideh and Vakilian, Ali}, title = {{Streaming Algorithms for Connectivity Augmentation}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {93:1--93:20}, 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.2024.93}, URN = {urn:nbn:de:0030-drops-202367}, doi = {10.4230/LIPIcs.ICALP.2024.93}, annote = {Keywords: streaming algorithms, connectivity augmentation} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yusuke Kobayashi and Tatsuya Terao. Subquadratic Submodular Maximization with a General Matroid Constraint. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{kobayashi_et_al:LIPIcs.ICALP.2024.100, author = {Kobayashi, Yusuke and Terao, Tatsuya}, title = {{Subquadratic Submodular Maximization with a General Matroid Constraint}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {100:1--100:19}, 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.2024.100}, URN = {urn:nbn:de:0030-drops-202437}, doi = {10.4230/LIPIcs.ICALP.2024.100}, annote = {Keywords: submodular maximization, matroid constraint, approximation algorithm, rounding algorithm, query complexity} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg. On the Cut-Query Complexity of Approximating Max-Cut. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{plevrakis_et_al:LIPIcs.ICALP.2024.115, author = {Plevrakis, Orestis and Ragavan, Seyoon and Weinberg, S. Matthew}, title = {{On the Cut-Query Complexity of Approximating Max-Cut}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {115:1--115:20}, 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.2024.115}, URN = {urn:nbn:de:0030-drops-202587}, doi = {10.4230/LIPIcs.ICALP.2024.115}, annote = {Keywords: query complexity, maximum cut, approximation algorithms, graph sparsification} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Kent Quanrud. Adaptive Sparsification for Matroid Intersection. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 118:1-118:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{quanrud:LIPIcs.ICALP.2024.118, author = {Quanrud, Kent}, title = {{Adaptive Sparsification for Matroid Intersection}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {118:1--118:20}, 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.2024.118}, URN = {urn:nbn:de:0030-drops-202614}, doi = {10.4230/LIPIcs.ICALP.2024.118}, annote = {Keywords: Matroid intersection, adaptive sparsification, multiplicative-weight udpates, primal-dual} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Sushant Sachdeva, Anvith Thudi, and Yibin Zhao. Better Sparsifiers for Directed Eulerian Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 119:1-119:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{sachdeva_et_al:LIPIcs.ICALP.2024.119, author = {Sachdeva, Sushant and Thudi, Anvith and Zhao, Yibin}, title = {{Better Sparsifiers for Directed Eulerian Graphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {119:1--119:20}, 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.2024.119}, URN = {urn:nbn:de:0030-drops-202628}, doi = {10.4230/LIPIcs.ICALP.2024.119}, annote = {Keywords: Graph algorithms, Linear algebra and computation, Discrepancy theory} }
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