Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)
Martin Farach-Colton, Fabian Daniel Kuhn, Ronitt Rubinfeld, and Przemysław Uznański. From Big Data Theory to Big Data Practice (Dagstuhl Seminar 23071). In Dagstuhl Reports, Volume 13, Issue 2, pp. 33-46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
@Article{farachcolton_et_al:DagRep.13.2.33, author = {Farach-Colton, Martin and Kuhn, Fabian Daniel and Rubinfeld, Ronitt and Uzna\'{n}ski, Przemys{\l}aw}, title = {{From Big Data Theory to Big Data Practice (Dagstuhl Seminar 23071)}}, pages = {33--46}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2023}, volume = {13}, number = {2}, editor = {Farach-Colton, Martin and Kuhn, Fabian Daniel and Rubinfeld, Ronitt and Uzna\'{n}ski, Przemys{\l}aw}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.33}, URN = {urn:nbn:de:0030-drops-191809}, doi = {10.4230/DagRep.13.2.33}, annote = {Keywords: external memory, local algorithms, sublinear algorithms} }
Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Spencer Compton, Slobodan Mitrović, and Ronitt Rubinfeld. New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 45:1-45:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
@InProceedings{compton_et_al:LIPIcs.ICALP.2023.45, author = {Compton, Spencer and Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt}, title = {{New Partitioning Techniques and Faster Algorithms for Approximate Interval Scheduling}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {45:1--45:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.45}, URN = {urn:nbn:de:0030-drops-180978}, doi = {10.4230/LIPIcs.ICALP.2023.45}, annote = {Keywords: interval scheduling, dynamic algorithms, local computation algorithms} }
Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)
Amartya Shankha Biswas, Talya Eden, Quanquan C. Liu, Ronitt Rubinfeld, and Slobodan Mitrović. Massively Parallel Algorithms for Small Subgraph Counting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 39:1-39:28, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
@InProceedings{biswas_et_al:LIPIcs.APPROX/RANDOM.2022.39, author = {Biswas, Amartya Shankha and Eden, Talya and Liu, Quanquan C. and Rubinfeld, Ronitt and Mitrovi\'{c}, Slobodan}, title = {{Massively Parallel Algorithms for Small Subgraph Counting}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {39:1--39:28}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-249-5}, ISSN = {1868-8969}, year = {2022}, volume = {245}, editor = {Chakrabarti, Amit and Swamy, Chaitanya}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.39}, URN = {urn:nbn:de:0030-drops-171619}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.39}, annote = {Keywords: triangle counting, massively parallel computation, clique counting, approximation algorithms, subgraph counting} }
Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Amartya Shankha Biswas, Edward Pyne, and Ronitt Rubinfeld. Local Access to Random Walks. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 24:1-24:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
@InProceedings{biswas_et_al:LIPIcs.ITCS.2022.24, author = {Biswas, Amartya Shankha and Pyne, Edward and Rubinfeld, Ronitt}, title = {{Local Access to Random Walks}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {24:1--24:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.24}, URN = {urn:nbn:de:0030-drops-156209}, doi = {10.4230/LIPIcs.ITCS.2022.24}, annote = {Keywords: sublinear time algorithms, random generation, local computation} }
Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Talya Eden, Saleet Mossel, and Ronitt Rubinfeld. Sampling Multiple Edges Efficiently. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 51:1-51:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{eden_et_al:LIPIcs.APPROX/RANDOM.2021.51, author = {Eden, Talya and Mossel, Saleet and Rubinfeld, Ronitt}, title = {{Sampling Multiple Edges Efficiently}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)}, pages = {51:1--51:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-207-5}, ISSN = {1868-8969}, year = {2021}, volume = {207}, editor = {Wootters, Mary and Sanit\`{a}, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.51}, URN = {urn:nbn:de:0030-drops-147441}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2021.51}, annote = {Keywords: Sampling edges, graph algorithm, sublinear algorithms} }
Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Amartya Shankha Biswas, Talya Eden, and Ronitt Rubinfeld. Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 55:1-55:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
@InProceedings{biswas_et_al:LIPIcs.APPROX/RANDOM.2021.55, author = {Biswas, Amartya Shankha and Eden, Talya and Rubinfeld, Ronitt}, title = {{Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)}, pages = {55:1--55:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-207-5}, ISSN = {1868-8969}, year = {2021}, volume = {207}, editor = {Wootters, Mary and Sanit\`{a}, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.55}, URN = {urn:nbn:de:0030-drops-147480}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2021.55}, annote = {Keywords: Sublinear time algorithms, Graph algorithms, Sampling subgraphs, Approximate counting} }
Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Dana Ron and Asaf Rosin. Almost Optimal Distribution-Free Sample-Based Testing of k-Modality. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 27:1-27:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{ron_et_al:LIPIcs.APPROX/RANDOM.2020.27, author = {Ron, Dana and Rosin, Asaf}, title = {{Almost Optimal Distribution-Free Sample-Based Testing of k-Modality}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {27:1--27:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-164-1}, ISSN = {1868-8969}, year = {2020}, volume = {176}, editor = {Byrka, Jaros{\l}aw and Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.27}, URN = {urn:nbn:de:0030-drops-126307}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.27}, annote = {Keywords: Sample-based property testing, Distribution-free property testing, k-modality} }
Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Rogers Epstein and Sandeep Silwal. Property Testing of LP-Type Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 98:1-98:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{epstein_et_al:LIPIcs.ICALP.2020.98, author = {Epstein, Rogers and Silwal, Sandeep}, title = {{Property Testing of LP-Type Problems}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {98:1--98:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.98}, URN = {urn:nbn:de:0030-drops-125056}, doi = {10.4230/LIPIcs.ICALP.2020.98}, annote = {Keywords: property pesting, LP-Type problems, random sampling} }
Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Amartya Shankha Biswas, Ronitt Rubinfeld, and Anak Yodpinyanee. Local Access to Huge Random Objects Through Partial Sampling. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 27:1-27:65, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{biswas_et_al:LIPIcs.ITCS.2020.27, author = {Biswas, Amartya Shankha and Rubinfeld, Ronitt and Yodpinyanee, Anak}, title = {{Local Access to Huge Random Objects Through Partial Sampling}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {27:1--27:65}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-134-4}, ISSN = {1868-8969}, year = {2020}, volume = {151}, editor = {Vidick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.27}, URN = {urn:nbn:de:0030-drops-117126}, doi = {10.4230/LIPIcs.ITCS.2020.27}, annote = {Keywords: sublinear time algorithms, random generation, local computation} }
Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Ronitt Rubinfeld and Arsen Vasilyan. Monotone Probability Distributions over the Boolean Cube Can Be Learned with Sublinear Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 28:1-28:34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{rubinfeld_et_al:LIPIcs.ITCS.2020.28, author = {Rubinfeld, Ronitt and Vasilyan, Arsen}, title = {{Monotone Probability Distributions over the Boolean Cube Can Be Learned with Sublinear Samples}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {28:1--28:34}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-134-4}, ISSN = {1868-8969}, year = {2020}, volume = {151}, editor = {Vidick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.28}, URN = {urn:nbn:de:0030-drops-117138}, doi = {10.4230/LIPIcs.ITCS.2020.28}, annote = {Keywords: Learning distributions, monotone probability distributions, estimating support size} }
Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Maryam Aliakbarpour and Sandeep Silwal. Testing Properties of Multiple Distributions with Few Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 69:1-69:41, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
@InProceedings{aliakbarpour_et_al:LIPIcs.ITCS.2020.69, author = {Aliakbarpour, Maryam and Silwal, Sandeep}, title = {{Testing Properties of Multiple Distributions with Few Samples}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {69:1--69:41}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-134-4}, ISSN = {1868-8969}, year = {2020}, volume = {151}, editor = {Vidick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.69}, URN = {urn:nbn:de:0030-drops-117545}, doi = {10.4230/LIPIcs.ITCS.2020.69}, annote = {Keywords: Hypothesis Testing, Property Testing, Distribution Testing, Identity Testing, Closeness Testing, Multiple Sources} }
Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Ronitt Rubinfeld and Arsen Vasilyan. Approximating the Noise Sensitivity of a Monotone Boolean Function. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 52:1-52:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
@InProceedings{rubinfeld_et_al:LIPIcs.APPROX-RANDOM.2019.52, author = {Rubinfeld, Ronitt and Vasilyan, Arsen}, title = {{Approximating the Noise Sensitivity of a Monotone Boolean Function}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)}, pages = {52:1--52:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-125-2}, ISSN = {1868-8969}, year = {2019}, volume = {145}, editor = {Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.52}, URN = {urn:nbn:de:0030-drops-112672}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.52}, annote = {Keywords: Monotone Boolean functions, noise sensitivity, influence} }
Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Merav Parter, Ronitt Rubinfeld, Ali Vakilian, and Anak Yodpinyanee. Local Computation Algorithms for Spanners. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 58:1-58:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
@InProceedings{parter_et_al:LIPIcs.ITCS.2019.58, author = {Parter, Merav and Rubinfeld, Ronitt and Vakilian, Ali and Yodpinyanee, Anak}, title = {{Local Computation Algorithms for Spanners}}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, pages = {58:1--58:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-095-8}, ISSN = {1868-8969}, year = {2019}, volume = {124}, editor = {Blum, Avrim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.58}, URN = {urn:nbn:de:0030-drops-101510}, doi = {10.4230/LIPIcs.ITCS.2019.58}, annote = {Keywords: Local Computation Algorithms, Sub-linear Algorithms, Graph Spanners} }
Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Piotr Indyk, Sepideh Mahabadi, Ronitt Rubinfeld, Jonathan Ullman, Ali Vakilian, and Anak Yodpinyanee. Fractional Set Cover in the Streaming Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 12:1-12:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
@InProceedings{indyk_et_al:LIPIcs.APPROX-RANDOM.2017.12, author = {Indyk, Piotr and Mahabadi, Sepideh and Rubinfeld, Ronitt and Ullman, Jonathan and Vakilian, Ali and Yodpinyanee, Anak}, title = {{Fractional Set Cover in the Streaming Model}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)}, pages = {12:1--12:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-044-6}, ISSN = {1868-8969}, year = {2017}, volume = {81}, editor = {Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.12}, URN = {urn:nbn:de:0030-drops-75613}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.12}, annote = {Keywords: Streaming Algorithms, Fractional Set Cover, LP relaxation, Multiplicative Weight Update} }
Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Ronitt Rubinfeld. Local Computation Algorithms (Invited Talk). In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, p. 3:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
@InProceedings{rubinfeld:LIPIcs.ICALP.2017.3, author = {Rubinfeld, Ronitt}, title = {{Local Computation Algorithms}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {3:1--3:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.3}, URN = {urn:nbn:de:0030-drops-75068}, doi = {10.4230/LIPIcs.ICALP.2017.3}, annote = {Keywords: Massive Data Sets, Approximate Solutions, Maximal Independent Set, Sparse Spanning Graphs} }
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