Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)
Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani. Faster Treewidth-Based Approximations for Wiener Index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{conrado_et_al:LIPIcs.SEA.2024.6, author = {Conrado, Giovanna Kobus and Goharshady, Amir Kafshdar and Hudec, Pavel and Li, Pingjiang and Motwani, Harshit Jitendra}, title = {{Faster Treewidth-Based Approximations for Wiener Index}}, booktitle = {22nd International Symposium on Experimental Algorithms (SEA 2024)}, pages = {6:1--6:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-325-6}, ISSN = {1868-8969}, year = {2024}, volume = {301}, editor = {Liberti, Leo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.6}, URN = {urn:nbn:de:0030-drops-203718}, doi = {10.4230/LIPIcs.SEA.2024.6}, annote = {Keywords: Computational Chemistry, Treewidth, Wiener Index} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha. NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{baraskar_et_al:LIPIcs.ICALP.2024.16, author = {Baraskar, Omkar and Dewan, Agrim and Saha, Chandan and Sinha, Pulkit}, title = {{NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {16:1--16:21}, 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.2024.16}, URN = {urn:nbn:de:0030-drops-201598}, doi = {10.4230/LIPIcs.ICALP.2024.16}, annote = {Keywords: Equivalence testing, MCSP, sparse polynomials, 3SAT} }
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)
Prantar Ghosh and Manuel Stoeckl. Low-Memory Algorithms for Online Edge Coloring. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{ghosh_et_al:LIPIcs.ICALP.2024.71, author = {Ghosh, Prantar and Stoeckl, Manuel}, title = {{Low-Memory Algorithms for Online Edge Coloring}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {71:1--71:19}, 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.2024.71}, URN = {urn:nbn:de:0030-drops-202146}, doi = {10.4230/LIPIcs.ICALP.2024.71}, annote = {Keywords: Edge coloring, streaming model, online algorithms} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Hamed Hatami, Kaave Hosseini, Shachar Lovett, and Anthony Ostuni. Refuting Approaches to the Log-Rank Conjecture for XOR Functions. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 82:1-82:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{hatami_et_al:LIPIcs.ICALP.2024.82, author = {Hatami, Hamed and Hosseini, Kaave and Lovett, Shachar and Ostuni, Anthony}, title = {{Refuting Approaches to the Log-Rank Conjecture for XOR Functions}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {82:1--82:11}, 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.2024.82}, URN = {urn:nbn:de:0030-drops-202252}, doi = {10.4230/LIPIcs.ICALP.2024.82}, annote = {Keywords: Communication complexity, log-rank conjecture, XOR functions, additive structure} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Klaus Heeger, Danny Hermelin, Matthias Mnich, and Dvir Shabtay. No Polynomial Kernels for Knapsack. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 83:1-83:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{heeger_et_al:LIPIcs.ICALP.2024.83, author = {Heeger, Klaus and Hermelin, Danny and Mnich, Matthias and Shabtay, Dvir}, title = {{No Polynomial Kernels for Knapsack}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {83:1--83:17}, 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.2024.83}, URN = {urn:nbn:de:0030-drops-202261}, doi = {10.4230/LIPIcs.ICALP.2024.83}, annote = {Keywords: Knapsack, polynomial kernels, compositions, number of different weights, number of different profits} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Aaron Potechin and Aaron Zhang. Bounds on the Total Coefficient Size of Nullstellensatz Proofs of the Pigeonhole Principle. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{potechin_et_al:LIPIcs.ICALP.2024.117, author = {Potechin, Aaron and Zhang, Aaron}, title = {{Bounds on the Total Coefficient Size of Nullstellensatz Proofs of the Pigeonhole Principle}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {117:1--117:20}, 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.2024.117}, URN = {urn:nbn:de:0030-drops-202604}, doi = {10.4230/LIPIcs.ICALP.2024.117}, annote = {Keywords: Proof complexity, Nullstellensatz, pigeonhole principle, coefficient size} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Raphael Douglas Giles, Vincent Jackson, and Christine Rizkallah. T-Rex: Termination of Recursive Functions Using Lexicographic Linear Combinations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 139:1-139:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{giles_et_al:LIPIcs.ICALP.2024.139, author = {Giles, Raphael Douglas and Jackson, Vincent and Rizkallah, Christine}, title = {{T-Rex: Termination of Recursive Functions Using Lexicographic Linear Combinations}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {139:1--139:19}, 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.2024.139}, URN = {urn:nbn:de:0030-drops-202827}, doi = {10.4230/LIPIcs.ICALP.2024.139}, annote = {Keywords: Termination, Recursive functions} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Quentin Guilmant, Engel Lefaucheux, Joël Ouaknine, and James Worrell. The 2-Dimensional Constraint Loop Problem Is Decidable. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 140:1-140:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{guilmant_et_al:LIPIcs.ICALP.2024.140, author = {Guilmant, Quentin and Lefaucheux, Engel and Ouaknine, Jo\"{e}l and Worrell, James}, title = {{The 2-Dimensional Constraint Loop Problem Is Decidable}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {140:1--140:21}, 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.2024.140}, URN = {urn:nbn:de:0030-drops-202831}, doi = {10.4230/LIPIcs.ICALP.2024.140}, annote = {Keywords: Linear Constraints Loops, Minkowski-Weyl, Convex Sets, Asymptotic Expansions} }
Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)
James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@Article{delgrande_et_al:DagMan.10.1.1, author = {Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank}, title = {{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}}, pages = {1--61}, journal = {Dagstuhl Manifestos}, ISSN = {2193-2433}, year = {2024}, volume = {10}, number = {1}, editor = {Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1}, URN = {urn:nbn:de:0030-drops-201403}, doi = {10.4230/DagMan.10.1.1}, annote = {Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic} }
Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1
Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer. Grounding Stream Reasoning Research. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 2:1-2:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@Article{bonte_et_al:TGDK.2.1.2, author = {Bonte, Pieter and Calbimonte, Jean-Paul and de Leng, Daniel and Dell'Aglio, Daniele and Della Valle, Emanuele and Eiter, Thomas and Giannini, Federico and Heintz, Fredrik and Schekotihin, Konstantin and Le-Phuoc, Danh and Mileo, Alessandra and Schneider, Patrik and Tommasini, Riccardo and Urbani, Jacopo and Ziffer, Giacomo}, title = {{Grounding Stream Reasoning Research}}, journal = {Transactions on Graph Data and Knowledge}, pages = {2:1--2:47}, ISSN = {2942-7517}, year = {2024}, volume = {2}, number = {1}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.2}, URN = {urn:nbn:de:0030-drops-198597}, doi = {10.4230/TGDK.2.1.2}, annote = {Keywords: Stream Reasoning, Stream Processing, RDF streams, Streaming Linked Data, Continuous query processing, Temporal Logics, High-performance computing, Databases} }
Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1
Pablo R. Fillottrani and C. Maria Keet. Logics for Conceptual Data Modelling: A Review. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 4:1-4:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@Article{fillottrani_et_al:TGDK.2.1.4, author = {Fillottrani, Pablo R. and Keet, C. Maria}, title = {{Logics for Conceptual Data Modelling: A Review}}, journal = {Transactions on Graph Data and Knowledge}, pages = {4:1--4:30}, ISSN = {2942-7517}, year = {2024}, volume = {2}, number = {1}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.4}, URN = {urn:nbn:de:0030-drops-198616}, doi = {10.4230/TGDK.2.1.4}, annote = {Keywords: Conceptual Data Modelling, EER, UML, Description Logics, OWL} }
Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Mrinal Kumar and Ben Lee Volk. A Polynomial Degree Bound on Equations for Non-Rigid Matrices and Small Linear Circuits. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 9:1-9:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{kumar_et_al:LIPIcs.ITCS.2021.9, author = {Kumar, Mrinal and Volk, Ben Lee}, title = {{A Polynomial Degree Bound on Equations for Non-Rigid Matrices and Small Linear Circuits}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {9:1--9:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-177-1}, ISSN = {1868-8969}, year = {2021}, volume = {185}, editor = {Lee, James R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.9}, URN = {urn:nbn:de:0030-drops-135486}, doi = {10.4230/LIPIcs.ITCS.2021.9}, annote = {Keywords: Rigid Matrices, Linear Circuits, Degree Bounds, Circuit Lower Bounds} }
Published in: LIPIcs, Volume 172, 20th International Workshop on Algorithms in Bioinformatics (WABI 2020)
Hooman Zabeti, Nick Dexter, Amir Hosein Safari, Nafiseh Sedaghat, Maxwell Libbrecht, and Leonid Chindelevitch. An Interpretable Classification Method for Predicting Drug Resistance in M. Tuberculosis. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{zabeti_et_al:LIPIcs.WABI.2020.2, author = {Zabeti, Hooman and Dexter, Nick and Safari, Amir Hosein and Sedaghat, Nafiseh and Libbrecht, Maxwell and Chindelevitch, Leonid}, title = {{An Interpretable Classification Method for Predicting Drug Resistance in M. Tuberculosis}}, booktitle = {20th International Workshop on Algorithms in Bioinformatics (WABI 2020)}, pages = {2:1--2:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-161-0}, ISSN = {1868-8969}, year = {2020}, volume = {172}, editor = {Kingsford, Carl and Pisanti, Nadia}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2020.2}, URN = {urn:nbn:de:0030-drops-127911}, doi = {10.4230/LIPIcs.WABI.2020.2}, annote = {Keywords: Drug resistance, whole-genome sequencing, interpretable machine learning, integer linear programming, rule-based learning} }
Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Amir M. Ben-Amram. Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity (Extended Abstract). In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 514-525, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
@InProceedings{benamram:LIPIcs.STACS.2013.514, author = {Ben-Amram, Amir M.}, title = {{Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity}}, booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)}, pages = {514--525}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-50-7}, ISSN = {1868-8969}, year = {2013}, volume = {20}, editor = {Portier, Natacha and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.514}, URN = {urn:nbn:de:0030-drops-39615}, doi = {10.4230/LIPIcs.STACS.2013.514}, annote = {Keywords: discrete-time dynamical systems, termination, Collatz problem} }
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