Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi. Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{lokshtanov_et_al:LIPIcs.APPROX/RANDOM.2024.6, author = {Lokshtanov, Daniel and Panolan, Fahad and Saurabh, Saket and Xue, Jie and Zehavi, Meirav}, title = {{Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {6:1--6:14}, 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.2024.6}, URN = {urn:nbn:de:0030-drops-209990}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.6}, annote = {Keywords: bipartization, geometric intersection graphs, approximation algorithms} }
Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)
Zhen Zhang, Junyu Huang, and Qilong Feng. Faster Approximation Schemes for (Constrained) k-Means with Outliers. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 84:1-84:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{zhang_et_al:LIPIcs.MFCS.2024.84, author = {Zhang, Zhen and Huang, Junyu and Feng, Qilong}, title = {{Faster Approximation Schemes for (Constrained) k-Means with Outliers}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {84:1--84:17}, 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.2024.84}, URN = {urn:nbn:de:0030-drops-206408}, doi = {10.4230/LIPIcs.MFCS.2024.84}, annote = {Keywords: Approximation algorithms, clustering} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Tanmay Inamdar, Pallavi Jain, Daniel Lokshtanov, Abhishek Sahu, Saket Saurabh, and Anannya Upasana. Satisfiability to Coverage in Presence of Fairness, Matroid, and Global Constraints. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 88:1-88:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{inamdar_et_al:LIPIcs.ICALP.2024.88, author = {Inamdar, Tanmay and Jain, Pallavi and Lokshtanov, Daniel and Sahu, Abhishek and Saurabh, Saket and Upasana, Anannya}, title = {{Satisfiability to Coverage in Presence of Fairness, Matroid, and Global Constraints}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {88:1--88:18}, 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.2024.88}, URN = {urn:nbn:de:0030-drops-202318}, doi = {10.4230/LIPIcs.ICALP.2024.88}, annote = {Keywords: Partial Vertex Cover, Max SAT, FPT Approximation, Matroids} }
Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)
Sayan Bandyapadhyay and Jie Xue. An O(n log n)-Time Approximation Scheme for Geometric Many-To-Many Matching. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2024.12, author = {Bandyapadhyay, Sayan and Xue, Jie}, title = {{An O(n log n)-Time Approximation Scheme for Geometric Many-To-Many Matching}}, booktitle = {40th International Symposium on Computational Geometry (SoCG 2024)}, pages = {12:1--12:15}, 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.2024.12}, URN = {urn:nbn:de:0030-drops-199577}, doi = {10.4230/LIPIcs.SoCG.2024.12}, annote = {Keywords: many-to-many matching, geometric optimization, approximation algorithms} }
Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)
Sayan Bandyapadhyay, Anil Maheshwari, Sasanka Roy, Michiel Smid, and Kasturi Varadarajan. Geometric Covering via Extraction Theorem. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{bandyapadhyay_et_al:LIPIcs.ITCS.2024.7, author = {Bandyapadhyay, Sayan and Maheshwari, Anil and Roy, Sasanka and Smid, Michiel and Varadarajan, Kasturi}, title = {{Geometric Covering via Extraction Theorem}}, booktitle = {15th Innovations in Theoretical Computer Science Conference (ITCS 2024)}, pages = {7:1--7:20}, 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.2024.7}, URN = {urn:nbn:de:0030-drops-195355}, doi = {10.4230/LIPIcs.ITCS.2024.7}, annote = {Keywords: Covering, Extraction theorem, Double-disks, Submodularity, Local search} }
Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Sayan Bandyapadhyay, Fedor V. Fomin, and Tanmay Inamdar. Coresets for Clustering in Geometric Intersection Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.10, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Inamdar, Tanmay}, title = {{Coresets for Clustering in Geometric Intersection Graphs}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {10:1--10:16}, 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.2023.10}, URN = {urn:nbn:de:0030-drops-178605}, doi = {10.4230/LIPIcs.SoCG.2023.10}, annote = {Keywords: k-median, k-means, clustering, coresets, geometric graphs} }
Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Sayan Bandyapadhyay, William Lochet, Saket Saurabh, and Jie Xue. Minimum-Membership Geometric Set Cover, Revisited. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.11, author = {Bandyapadhyay, Sayan and Lochet, William and Saurabh, Saket and Xue, Jie}, title = {{Minimum-Membership Geometric Set Cover, Revisited}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {11:1--11:14}, 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.2023.11}, URN = {urn:nbn:de:0030-drops-178610}, doi = {10.4230/LIPIcs.SoCG.2023.11}, annote = {Keywords: geometric set cover, geometric optimization, approximation algorithms} }
Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Sayan Bandyapadhyay, William Lochet, and Saket Saurabh. FPT Constant-Approximations for Capacitated Clustering to Minimize the Sum of Cluster Radii. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.12, author = {Bandyapadhyay, Sayan and Lochet, William and Saurabh, Saket}, title = {{FPT Constant-Approximations for Capacitated Clustering to Minimize the Sum of Cluster Radii}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {12:1--12:14}, 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.2023.12}, URN = {urn:nbn:de:0030-drops-178628}, doi = {10.4230/LIPIcs.SoCG.2023.12}, annote = {Keywords: Clustering, FPT-approximation} }
Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)
Sayan Bandyapadhyay, Fedor V. Fomin, Petr A. Golovach, Nidhi Purohit, and Kirill Simonov. FPT Approximation for Fair Minimum-Load Clustering. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{bandyapadhyay_et_al:LIPIcs.IPEC.2022.4, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Golovach, Petr A. and Purohit, Nidhi and Simonov, Kirill}, title = {{FPT Approximation for Fair Minimum-Load Clustering}}, booktitle = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)}, pages = {4:1--4:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-260-0}, ISSN = {1868-8969}, year = {2022}, volume = {249}, editor = {Dell, Holger and Nederlof, Jesper}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.4}, URN = {urn:nbn:de:0030-drops-173600}, doi = {10.4230/LIPIcs.IPEC.2022.4}, annote = {Keywords: fair clustering, load balancing, parameterized approximation} }
Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)
Sayan Bandyapadhyay, William Lochet, Daniel Lokshtanov, Saket Saurabh, and Jie Xue. True Contraction Decomposition and Almost ETH-Tight Bipartization for Unit-Disk Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2022.11, author = {Bandyapadhyay, Sayan and Lochet, William and Lokshtanov, Daniel and Saurabh, Saket and Xue, Jie}, title = {{True Contraction Decomposition and Almost ETH-Tight Bipartization for Unit-Disk Graphs}}, booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)}, pages = {11:1--11:16}, 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.2022.11}, URN = {urn:nbn:de:0030-drops-160190}, doi = {10.4230/LIPIcs.SoCG.2022.11}, annote = {Keywords: unit-disk graphs, tree decomposition, contraction decomposition, bipartization} }
Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Sayan Bandyapadhyay, Anil Maheshwari, and Michiel Smid. Exact and Approximation Algorithms for Many-To-Many Point Matching in the Plane. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{bandyapadhyay_et_al:LIPIcs.ISAAC.2021.44, author = {Bandyapadhyay, Sayan and Maheshwari, Anil and Smid, Michiel}, title = {{Exact and Approximation Algorithms for Many-To-Many Point Matching in the Plane}}, booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)}, pages = {44:1--44:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-214-3}, ISSN = {1868-8969}, year = {2021}, volume = {212}, editor = {Ahn, Hee-Kap and Sadakane, Kunihiko}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.44}, URN = {urn:nbn:de:0030-drops-154779}, doi = {10.4230/LIPIcs.ISAAC.2021.44}, annote = {Keywords: Many-to-many matching, bipartite, planar, geometric, approximation} }
Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Sayan Bandyapadhyay, Fedor V. Fomin, Petr A. Golovach, and Kirill Simonov. Parameterized Complexity of Feature Selection for Categorical Data Clustering. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{bandyapadhyay_et_al:LIPIcs.MFCS.2021.14, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Golovach, Petr A. and Simonov, Kirill}, title = {{Parameterized Complexity of Feature Selection for Categorical Data Clustering}}, booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)}, pages = {14:1--14:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-201-3}, ISSN = {1868-8969}, year = {2021}, volume = {202}, editor = {Bonchi, Filippo and Puglisi, Simon J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.14}, URN = {urn:nbn:de:0030-drops-144544}, doi = {10.4230/LIPIcs.MFCS.2021.14}, annote = {Keywords: Robust clustering, PCA, Low rank approximation, Hypergraph enumeration} }
Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Sayan Bandyapadhyay, Fedor V. Fomin, and Kirill Simonov. On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{bandyapadhyay_et_al:LIPIcs.ICALP.2021.23, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Simonov, Kirill}, title = {{On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {23:1--23:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.23}, URN = {urn:nbn:de:0030-drops-140923}, doi = {10.4230/LIPIcs.ICALP.2021.23}, annote = {Keywords: fair clustering, coresets, approximation algorithms} }
Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)
Sayan Bandyapadhyay. Improved Bounds for Metric Capacitated Covering Problems. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{bandyapadhyay:LIPIcs.ESA.2020.9, author = {Bandyapadhyay, Sayan}, title = {{Improved Bounds for Metric Capacitated Covering Problems}}, booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)}, pages = {9:1--9:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-162-7}, ISSN = {1868-8969}, year = {2020}, volume = {173}, editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.9}, URN = {urn:nbn:de:0030-drops-128759}, doi = {10.4230/LIPIcs.ESA.2020.9}, annote = {Keywords: Capacitated covering, approximation algorithms, bicriteria approximation, LP rounding} }
Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Sayan Bandyapadhyay. On Perturbation Resilience of Non-Uniform k-Center. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{bandyapadhyay:LIPIcs.APPROX/RANDOM.2020.31, author = {Bandyapadhyay, Sayan}, title = {{On Perturbation Resilience of Non-Uniform k-Center}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {31:1--31:22}, 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.2020.31}, URN = {urn:nbn:de:0030-drops-126347}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.31}, annote = {Keywords: Non-Uniform k-center, stability, clustering, perturbation resilience} }
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