Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Alexander Golovnev, Zeyu Guo, Pooya Hatami, Satyajeet Nagargoje, and Chao Yan. Hilbert Functions and Low-Degree Randomness Extractors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 41:1-41:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{golovnev_et_al:LIPIcs.APPROX/RANDOM.2024.41, author = {Golovnev, Alexander and Guo, Zeyu and Hatami, Pooya and Nagargoje, Satyajeet and Yan, Chao}, title = {{Hilbert Functions and Low-Degree Randomness Extractors}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {41:1--41:24}, 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.2024.41}, URN = {urn:nbn:de:0030-drops-210345}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.41}, annote = {Keywords: Extractors, Dispersers, Circuits, Hilbert Function, Randomness, Low Degree Polynomials} }
Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)
Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, and Nadia Pisanti. A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{ascone_et_al:LIPIcs.WABI.2024.14, author = {Ascone, Rocco and Bernardini, Giulia and Conte, Alessio and Equi, Massimo and Gabory, Esteban and Grossi, Roberto and Pisanti, Nadia}, title = {{A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs}}, booktitle = {24th International Workshop on Algorithms in Bioinformatics (WABI 2024)}, pages = {14:1--14:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-340-9}, ISSN = {1868-8969}, year = {2024}, volume = {312}, editor = {Pissis, Solon P. and Sung, Wing-Kin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.14}, URN = {urn:nbn:de:0030-drops-206586}, doi = {10.4230/LIPIcs.WABI.2024.14}, annote = {Keywords: Pangenomics, pattern matching, degenerate string, founder graph, fine-grained complexity} }
Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)
Karthik Gajulapalli, Alexander Golovnev, and Samuel King. On the Power of Adaptivity for Function Inversion. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 5:1-5:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{gajulapalli_et_al:LIPIcs.ITC.2024.5, author = {Gajulapalli, Karthik and Golovnev, Alexander and King, Samuel}, title = {{On the Power of Adaptivity for Function Inversion}}, booktitle = {5th Conference on Information-Theoretic Cryptography (ITC 2024)}, pages = {5:1--5:10}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-333-1}, ISSN = {1868-8969}, year = {2024}, volume = {304}, editor = {Aggarwal, Divesh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.5}, URN = {urn:nbn:de:0030-drops-205137}, doi = {10.4230/LIPIcs.ITC.2024.5}, annote = {Keywords: Function Inversion, Non-Adaptive lower bounds, Communication Complexity} }
Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)
Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7, author = {Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik}, title = {{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}}, booktitle = {39th Computational Complexity Conference (CCC 2024)}, pages = {7:1--7:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-331-7}, ISSN = {1868-8969}, year = {2024}, volume = {300}, editor = {Santhanam, Rahul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7}, URN = {urn:nbn:de:0030-drops-204035}, doi = {10.4230/LIPIcs.CCC.2024.7}, annote = {Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi. Optimal Bounds for Distinct Quartics. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2024.39, author = {Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Ghazawi, Samah}, title = {{Optimal Bounds for Distinct Quartics}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {39:1--39:17}, 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.2024.39}, URN = {urn:nbn:de:0030-drops-201823}, doi = {10.4230/LIPIcs.ICALP.2024.39}, annote = {Keywords: 2D strings, quartics, repetitions, periodicity} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Sami Davies, Benjamin Moseley, and Heather Newman. Simultaneously Approximating All 𝓁_p-Norms in Correlation Clustering. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 52:1-52:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{davies_et_al:LIPIcs.ICALP.2024.52, author = {Davies, Sami and Moseley, Benjamin and Newman, Heather}, title = {{Simultaneously Approximating All 𝓁\underlinep-Norms in Correlation Clustering}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {52:1--52:20}, 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.2024.52}, URN = {urn:nbn:de:0030-drops-201950}, doi = {10.4230/LIPIcs.ICALP.2024.52}, annote = {Keywords: Approximation algorithms, correlation clustering, all-norms, lp-norms} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Aditi Dudeja. Decremental Matching in General Weighted Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{dudeja:LIPIcs.ICALP.2024.59, author = {Dudeja, Aditi}, title = {{Decremental Matching in General Weighted Graphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {59:1--59:20}, 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.2024.59}, URN = {urn:nbn:de:0030-drops-202020}, doi = {10.4230/LIPIcs.ICALP.2024.59}, annote = {Keywords: Weighted Matching, Dynamic Algorithms, Adaptive Adversary} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Tsvi Kopelowitz, Ariel Korin, and Liam Roditty. On the Space Usage of Approximate Distance Oracles with Sub-2 Stretch. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 101:1-101:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{kopelowitz_et_al:LIPIcs.ICALP.2024.101, author = {Kopelowitz, Tsvi and Korin, Ariel and Roditty, Liam}, title = {{On the Space Usage of Approximate Distance Oracles with Sub-2 Stretch}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {101:1--101:18}, 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.2024.101}, URN = {urn:nbn:de:0030-drops-202443}, doi = {10.4230/LIPIcs.ICALP.2024.101}, annote = {Keywords: Graph algorithms, Approximate distance oracle, data structures, shortest path} }
Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)
Matan Kraus, Moshe Lewenstein, Alexandru Popa, Ely Porat, and Yonathan Sadia. String Factorization via Prefix Free Families. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 19:1-19:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{kraus_et_al:LIPIcs.CPM.2023.19, author = {Kraus, Matan and Lewenstein, Moshe and Popa, Alexandru and Porat, Ely and Sadia, Yonathan}, title = {{String Factorization via Prefix Free Families}}, booktitle = {34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)}, pages = {19:1--19:10}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-276-1}, ISSN = {1868-8969}, year = {2023}, volume = {259}, editor = {Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.19}, URN = {urn:nbn:de:0030-drops-179738}, doi = {10.4230/LIPIcs.CPM.2023.19}, annote = {Keywords: string factorization, NP-hard problem, approximation algorithm} }
Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)
Avivit Levy, Ely Porat, and B. Riva Shalom. Partial Permutations Comparison, Maintenance and Applications. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{levy_et_al:LIPIcs.CPM.2022.10, author = {Levy, Avivit and Porat, Ely and Shalom, B. Riva}, title = {{Partial Permutations Comparison, Maintenance and Applications}}, booktitle = {33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)}, pages = {10:1--10:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-234-1}, ISSN = {1868-8969}, year = {2022}, volume = {223}, editor = {Bannai, Hideo and Holub, Jan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.10}, URN = {urn:nbn:de:0030-drops-161376}, doi = {10.4230/LIPIcs.CPM.2022.10}, annote = {Keywords: Partial permutations, Partial words, Genes comparison, Color transformation, Dictionary matching with gaps, Parameterized matching, SETH hypothesis} }
Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)
Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. The Dynamic k-Mismatch Problem. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{clifford_et_al:LIPIcs.CPM.2022.18, author = {Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw}, title = {{The Dynamic k-Mismatch Problem}}, booktitle = {33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)}, pages = {18:1--18:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-234-1}, ISSN = {1868-8969}, year = {2022}, volume = {223}, editor = {Bannai, Hideo and Holub, Jan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.18}, URN = {urn:nbn:de:0030-drops-161454}, doi = {10.4230/LIPIcs.CPM.2022.18}, annote = {Keywords: Pattern matching, Hamming distance, dynamic algorithms} }
Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)
Michael A. Bender, Tsvi Kopelowitz, William Kuszmaul, Ely Porat, and Clifford Stein. Incremental Edge Orientation in Forests. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{bender_et_al:LIPIcs.ESA.2021.12, author = {Bender, Michael A. and Kopelowitz, Tsvi and Kuszmaul, William and Porat, Ely and Stein, Clifford}, title = {{Incremental Edge Orientation in Forests}}, booktitle = {29th Annual European Symposium on Algorithms (ESA 2021)}, pages = {12:1--12:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-204-4}, ISSN = {1868-8969}, year = {2021}, volume = {204}, editor = {Mutzel, Petra and Pagh, Rasmus 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.2021.12}, URN = {urn:nbn:de:0030-drops-145933}, doi = {10.4230/LIPIcs.ESA.2021.12}, annote = {Keywords: edge orientation, graph algorithms, Cuckoo hashing, hash functions} }
Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)
Samuel McCauley. Approximate Similarity Search Under Edit Distance Using Locality-Sensitive Hashing. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{mccauley:LIPIcs.ICDT.2021.21, author = {McCauley, Samuel}, title = {{Approximate Similarity Search Under Edit Distance Using Locality-Sensitive Hashing}}, booktitle = {24th International Conference on Database Theory (ICDT 2021)}, pages = {21:1--21:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-179-5}, ISSN = {1868-8969}, year = {2021}, volume = {186}, editor = {Yi, Ke and Wei, Zhewei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.21}, URN = {urn:nbn:de:0030-drops-137299}, doi = {10.4230/LIPIcs.ICDT.2021.21}, annote = {Keywords: edit distance, approximate pattern matching, approximate nearest neighbor, similarity search, locality-sensitive hashing} }
Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, Ely Porat, and Przemysław Uznański. Improved Circular k-Mismatch Sketches. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 46:1-46:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{golan_et_al:LIPIcs.APPROX/RANDOM.2020.46, author = {Golan, Shay and Kociumaka, Tomasz and Kopelowitz, Tsvi and Porat, Ely and Uzna\'{n}ski, Przemys{\l}aw}, title = {{Improved Circular k-Mismatch Sketches}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {46:1--46:24}, 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.2020.46}, URN = {urn:nbn:de:0030-drops-126492}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.46}, annote = {Keywords: Hamming distance, k-mismatch, sketches, rotation, cyclic shift, communication complexity} }
Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, and Ely Porat. The Streaming k-Mismatch Problem: Tradeoffs Between Space and Total Time. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{golan_et_al:LIPIcs.CPM.2020.15, author = {Golan, Shay and Kociumaka, Tomasz and Kopelowitz, Tsvi and Porat, Ely}, title = {{The Streaming k-Mismatch Problem: Tradeoffs Between Space and Total Time}}, booktitle = {31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)}, pages = {15:1--15:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-149-8}, ISSN = {1868-8969}, year = {2020}, volume = {161}, editor = {G{\o}rtz, Inge Li and Weimann, Oren}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.15}, URN = {urn:nbn:de:0030-drops-121406}, doi = {10.4230/LIPIcs.CPM.2020.15}, annote = {Keywords: Streaming pattern matching, Hamming distance, k-mismatch} }
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