Parameterized complexity of categorical clustering with size constraints
In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Pa...
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| Veröffentlicht in: | Journal of computer and system sciences Jg. 136; S. 171 - 194 |
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01.09.2023
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| Abstract | In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Panolan [ICALP 2018] proved that the problem is fixed-parameter tractable for the binary case Σ={0,1}. We extend this algorithmic result to a popular capacitated clustering model, where in addition the sizes of the clusters are lower and upper bounded by integer parameters p and q, respectively. Our main theorem is that the problem is solvable in time 2O(BlogB)|Σ|B⋅(mn)O(1). |
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| AbstractList | In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Panolan [ICALP 2018] proved that the problem is fixed-parameter tractable for the binary case Σ={0,1}. We extend this algorithmic result to a popular capacitated clustering model, where in addition the sizes of the clusters are lower and upper bounded by integer parameters p and q, respectively. Our main theorem is that the problem is solvable in time 2O(BlogB)|Σ|B⋅(mn)O(1). |
| Author | Golovach, Petr A. Purohit, Nidhi Fomin, Fedor V. |
| Author_xml | – sequence: 1 givenname: Fedor V. surname: Fomin fullname: Fomin, Fedor V. email: fedor.fomin@uib.no – sequence: 2 givenname: Petr A. orcidid: 0000-0002-2619-2990 surname: Golovach fullname: Golovach, Petr A. email: petr.golovach@uib.no – sequence: 3 givenname: Nidhi surname: Purohit fullname: Purohit, Nidhi email: nidhi.purohit@uib.no |
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| Keywords | k-median Fixed-parameterized algorithm Categorical clustering Kernelization |
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| References | Lynch, Horton, Horton (br0280) 1999 Nielsen (br0330) 1992 Kleinberg, Papadimitriou, Raghavan (br0240) 2004; 51 Alon, Yuster, Zwick (br0020) 1995; 42 Otter (br0350) 1948; 49 Naor, Schulman, Srinivasan (br0320) 1995 Miettinen, Mielikäinen, Gionis, Das, Mannila (br0310) 2008; 20 Rösner, Schmidt (br0360) 2018 Aggarwal, Panigrahy, Feder, Thomas, Kenthapadi, Khuller, Zhu (br0010) 2010; 6 Ghiasi, Srivastava, Yang, Sarrafzadeh (br0220) 2002; 2 Downey, Fellows (br0150) 2013 Byrka, Rybicki, Uniyal (br0070) 2016; vol. 9682 Fomin, Golovach, Panolan (br0190) 2020; 34 Ban, Bhattiprolu, Bringmann, Kolev, Lee, Woodruff (br0040) 2019 Garey, Johnson (br0210) 1979 Banerjee, Ghosh (br0050) 2008 Feige (br0160) 2014 Kuhn (br0250) 1955; 2 Demirci, Li (br0140) 2016 Byrka, Fleszar, Rybicki, Spoerhase (br0060) 2015 Gupta, Younis (br0230) 2003; vol. 3 Yang, Padmanabhan (br0390) 2003 Li (br0260) 2017; 13 Cohen-Addad, Li (br0120) 2019; vol. 132 Malinen, Fränti (br0290) 2014; vol. 8621 Wright, Richmond, Odlyzko, McKay (br0380) 1986; 15 Chen, Li, Liang, Wang (br0090) 2016; 75 Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh (br0130) 2015 Charikar, Guha, Tardos, Shmoys (br0080) 2002; 65 Cilibrasi, van Iersel, Kelk, Tromp (br0110) 2007; 49 Fomin, Lokshtanov, Saurabh, Zehavi (br0170) 2019 Baeza-Yates, Ribeiro-Neto (br0030) 1999; vol. 463 Chuzhoy, Rabani (br0100) 2005 Fomin, Golovach, Lokshtanov, Panolan, Saurabh (br0180) 2020; 16 Ostrovsky, Rabani (br0340) 2002; 49 Lovász, Plummer (br0270) 2009 Marx (br0300) 2008; 38 Vallejo-Huanga, Morillo, Ferri (br0370) 2017; vol. 108 Fomin, Golovach, Simonov (br0200) 2021; 117 Fomin (10.1016/j.jcss.2023.03.006_br0180) 2020; 16 Kuhn (10.1016/j.jcss.2023.03.006_br0250) 1955; 2 Otter (10.1016/j.jcss.2023.03.006_br0350) 1948; 49 Byrka (10.1016/j.jcss.2023.03.006_br0070) 2016; vol. 9682 Marx (10.1016/j.jcss.2023.03.006_br0300) 2008; 38 Rösner (10.1016/j.jcss.2023.03.006_br0360) 2018 Banerjee (10.1016/j.jcss.2023.03.006_br0050) 2008 Cygan (10.1016/j.jcss.2023.03.006_br0130) 2015 Ban (10.1016/j.jcss.2023.03.006_br0040) 2019 Baeza-Yates (10.1016/j.jcss.2023.03.006_br0030) 1999; vol. 463 Ghiasi (10.1016/j.jcss.2023.03.006_br0220) 2002; 2 Fomin (10.1016/j.jcss.2023.03.006_br0190) 2020; 34 Vallejo-Huanga (10.1016/j.jcss.2023.03.006_br0370) 2017; vol. 108 Chuzhoy (10.1016/j.jcss.2023.03.006_br0100) 2005 Lynch (10.1016/j.jcss.2023.03.006_br0280) 1999 Feige (10.1016/j.jcss.2023.03.006_br0160) Miettinen (10.1016/j.jcss.2023.03.006_br0310) 2008; 20 Kleinberg (10.1016/j.jcss.2023.03.006_br0240) 2004; 51 Charikar (10.1016/j.jcss.2023.03.006_br0080) 2002; 65 Gupta (10.1016/j.jcss.2023.03.006_br0230) 2003; vol. 3 Demirci (10.1016/j.jcss.2023.03.006_br0140) 2016 Nielsen (10.1016/j.jcss.2023.03.006_br0330) 1992 Malinen (10.1016/j.jcss.2023.03.006_br0290) 2014; vol. 8621 Naor (10.1016/j.jcss.2023.03.006_br0320) 1995 Byrka (10.1016/j.jcss.2023.03.006_br0060) 2015 Cohen-Addad (10.1016/j.jcss.2023.03.006_br0120) 2019; vol. 132 Lovász (10.1016/j.jcss.2023.03.006_br0270) 2009 Garey (10.1016/j.jcss.2023.03.006_br0210) 1979 Aggarwal (10.1016/j.jcss.2023.03.006_br0010) 2010; 6 Alon (10.1016/j.jcss.2023.03.006_br0020) 1995; 42 Downey (10.1016/j.jcss.2023.03.006_br0150) 2013 Yang (10.1016/j.jcss.2023.03.006_br0390) 2003 Fomin (10.1016/j.jcss.2023.03.006_br0200) 2021; 117 Chen (10.1016/j.jcss.2023.03.006_br0090) 2016; 75 Li (10.1016/j.jcss.2023.03.006_br0260) 2017; 13 Ostrovsky (10.1016/j.jcss.2023.03.006_br0340) 2002; 49 Cilibrasi (10.1016/j.jcss.2023.03.006_br0110) 2007; 49 Fomin (10.1016/j.jcss.2023.03.006_br0170) 2019 Wright (10.1016/j.jcss.2023.03.006_br0380) 1986; 15 |
| References_xml | – start-page: 952 year: 2005 end-page: 958 ident: br0100 article-title: Approximating k-median with non-uniform capacities publication-title: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005 – year: 2014 ident: br0160 article-title: NP-hardness of hypercube 2-segmentation – volume: 49 start-page: 583 year: 1948 end-page: 599 ident: br0350 article-title: The number of trees publication-title: Ann. Math. (2) – start-page: 411 year: 2003 end-page: 418 ident: br0390 article-title: Segmenting customer transactions using a pattern-based clustering approach publication-title: Proceedings of the 3rd IEEE International Conference on Data Mining (ICDM) – start-page: 182 year: 1995 end-page: 191 ident: br0320 article-title: Splitters and near-optimal derandomization publication-title: Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS) – volume: 13 start-page: 22:1 year: 2017 end-page: 22:18 ident: br0260 article-title: On uniform capacitated k-median beyond the natural LP relaxation publication-title: ACM Trans. Algorithms – volume: vol. 463 year: 1999 ident: br0030 article-title: Modern Information Retrieval – start-page: 747 year: 2019 end-page: 766 ident: br0040 article-title: A PTAS for publication-title: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019 – year: 2013 ident: br0150 article-title: Fundamentals of Parameterized Complexity publication-title: Texts in Computer Science – volume: 2 start-page: 258 year: 2002 end-page: 269 ident: br0220 article-title: Optimal energy aware clustering in sensor networks publication-title: Sensors – volume: vol. 3 start-page: 1848 year: 2003 end-page: 1852 ident: br0230 article-title: Load-balanced clustering of wireless sensor networks publication-title: IEEE International Conference on Communications (ICC) – year: 1999 ident: br0280 article-title: Web Style Guide: Basic Design Principles for Creating Web Sites – volume: 6 year: 2010 ident: br0010 article-title: Achieving anonymity via clustering publication-title: ACM Trans. Algorithms – volume: 51 start-page: 263 year: 2004 end-page: 280 ident: br0240 article-title: Segmentation problems publication-title: J. ACM – year: 1979 ident: br0210 article-title: Computers and Intractability, A Guide to the Theory of NP-Completeness – volume: vol. 9682 start-page: 262 year: 2016 end-page: 274 ident: br0070 article-title: An approximation algorithm for uniform capacitated k-median problem with publication-title: Integer Programming and Combinatorial Optimization - 18th International Conference – start-page: 73:1 year: 2016 end-page: 73:14 ident: br0140 article-title: Constant approximation for capacitated k-median with publication-title: 43rd International Colloquium on Automata, Languages, and Programming – volume: 75 start-page: 27 year: 2016 end-page: 52 ident: br0090 article-title: Matroid and knapsack center problems publication-title: Algorithmica – volume: 20 start-page: 1348 year: 2008 end-page: 1362 ident: br0310 article-title: The discrete basis problem publication-title: IEEE Trans. Knowl. Data Eng. – volume: 16 start-page: 12:1 year: 2020 end-page: 12:39 ident: br0180 article-title: Approximation schemes for low-rank binary matrix approximation problems publication-title: ACM Trans. Algorithms – volume: 34 start-page: 478 year: 2020 end-page: 532 ident: br0190 article-title: Parameterized low-rank binary matrix approximation publication-title: Data Min. Knowl. Discov. – volume: 38 start-page: 1382 year: 2008 end-page: 1410 ident: br0300 article-title: Closest substring problems with small distances publication-title: SIAM J. Comput. – volume: 15 start-page: 540 year: 1986 end-page: 548 ident: br0380 article-title: Constant time generation of free trees publication-title: SIAM J. Comput. – year: 2019 ident: br0170 article-title: Kernelization – start-page: 171 year: 2008 end-page: 200 ident: br0050 article-title: Clustering with balancing constraints publication-title: Constrained Clustering: Advances in Algorithms, Theory, and Applications – volume: 117 start-page: 50 year: 2021 end-page: 74 ident: br0200 article-title: Parameterized k-clustering: tractability island publication-title: J. Comput. Syst. Sci. – volume: vol. 8621 start-page: 32 year: 2014 end-page: 41 ident: br0290 article-title: Balanced k-means for clustering publication-title: Structural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshop – volume: vol. 132 start-page: 41:1 year: 2019 end-page: 41:14 ident: br0120 article-title: On the fixed-parameter tractability of capacitated clustering publication-title: 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 – volume: 65 start-page: 129 year: 2002 end-page: 149 ident: br0080 article-title: A constant-factor approximation algorithm for the k-median problem publication-title: J. Comput. Syst. Sci. – volume: 42 start-page: 844 year: 1995 end-page: 856 ident: br0020 article-title: Color-coding publication-title: J. ACM – volume: 49 start-page: 139 year: 2002 end-page: 156 ident: br0340 article-title: Polynomial-time approximation schemes for geometric min-sum median clustering publication-title: J. ACM – start-page: 722 year: 2015 end-page: 736 ident: br0060 article-title: Bi-factor approximation algorithms for hard capacitated k-median problems publication-title: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 – volume: 49 start-page: 13 year: 2007 end-page: 36 ident: br0110 article-title: The complexity of the single individual SNP haplotyping problem publication-title: Algorithmica – year: 2009 ident: br0270 article-title: Matching Theory – year: 1992 ident: br0330 article-title: Category Management: Positioning Your Organization to Win – volume: vol. 108 start-page: 325 year: 2017 end-page: 334 ident: br0370 article-title: Semi-supervised clustering algorithms for grouping scientific articles publication-title: International Conference on Computational Science (ICCS) – year: 2018 ident: br0360 article-title: Privacy preserving clustering with constraints publication-title: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) – volume: 2 start-page: 83 year: 1955 end-page: 97 ident: br0250 article-title: The Hungarian method for the assignment problem publication-title: Nav. Res. Logist. Q. – year: 2015 ident: br0130 article-title: Parameterized Algorithms – volume: 2 start-page: 83 issn: 0028-1441 year: 1955 ident: 10.1016/j.jcss.2023.03.006_br0250 article-title: The Hungarian method for the assignment problem publication-title: Nav. Res. Logist. Q. doi: 10.1002/nav.3800020109 – volume: vol. 3 start-page: 1848 year: 2003 ident: 10.1016/j.jcss.2023.03.006_br0230 article-title: Load-balanced clustering of wireless sensor networks – start-page: 182 year: 1995 ident: 10.1016/j.jcss.2023.03.006_br0320 article-title: Splitters and near-optimal derandomization – start-page: 747 year: 2019 ident: 10.1016/j.jcss.2023.03.006_br0040 article-title: A PTAS for ℓp-low rank approximation – volume: 16 start-page: 12:1 issue: 1 year: 2020 ident: 10.1016/j.jcss.2023.03.006_br0180 article-title: Approximation schemes for low-rank binary matrix approximation problems publication-title: ACM Trans. Algorithms doi: 10.1145/3365653 – volume: vol. 463 year: 1999 ident: 10.1016/j.jcss.2023.03.006_br0030 – volume: vol. 8621 start-page: 32 year: 2014 ident: 10.1016/j.jcss.2023.03.006_br0290 article-title: Balanced k-means for clustering – volume: 42 start-page: 844 issue: 4 year: 1995 ident: 10.1016/j.jcss.2023.03.006_br0020 article-title: Color-coding publication-title: J. ACM doi: 10.1145/210332.210337 – volume: 65 start-page: 129 issue: 1 year: 2002 ident: 10.1016/j.jcss.2023.03.006_br0080 article-title: A constant-factor approximation algorithm for the k-median problem publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2002.1882 – volume: 75 start-page: 27 issue: 1 year: 2016 ident: 10.1016/j.jcss.2023.03.006_br0090 article-title: Matroid and knapsack center problems publication-title: Algorithmica doi: 10.1007/s00453-015-0010-1 – year: 2019 ident: 10.1016/j.jcss.2023.03.006_br0170 – start-page: 411 year: 2003 ident: 10.1016/j.jcss.2023.03.006_br0390 article-title: Segmenting customer transactions using a pattern-based clustering approach – year: 1999 ident: 10.1016/j.jcss.2023.03.006_br0280 – year: 1992 ident: 10.1016/j.jcss.2023.03.006_br0330 – volume: 49 start-page: 139 issn: 0004-5411 issue: 2 year: 2002 ident: 10.1016/j.jcss.2023.03.006_br0340 article-title: Polynomial-time approximation schemes for geometric min-sum median clustering publication-title: J. ACM doi: 10.1145/506147.506149 – volume: 13 start-page: 22:1 issue: 2 year: 2017 ident: 10.1016/j.jcss.2023.03.006_br0260 article-title: On uniform capacitated k-median beyond the natural LP relaxation publication-title: ACM Trans. Algorithms doi: 10.1145/2983633 – start-page: 73:1 year: 2016 ident: 10.1016/j.jcss.2023.03.006_br0140 article-title: Constant approximation for capacitated k-median with (1+ε)-capacity violation – volume: 51 start-page: 263 issn: 0004-5411 issue: 2 year: 2004 ident: 10.1016/j.jcss.2023.03.006_br0240 article-title: Segmentation problems publication-title: J. ACM doi: 10.1145/972639.972644 – volume: vol. 108 start-page: 325 year: 2017 ident: 10.1016/j.jcss.2023.03.006_br0370 article-title: Semi-supervised clustering algorithms for grouping scientific articles – year: 2013 ident: 10.1016/j.jcss.2023.03.006_br0150 article-title: Fundamentals of Parameterized Complexity – volume: 20 start-page: 1348 issue: 10 year: 2008 ident: 10.1016/j.jcss.2023.03.006_br0310 article-title: The discrete basis problem publication-title: IEEE Trans. Knowl. Data Eng. doi: 10.1109/TKDE.2008.53 – volume: 117 start-page: 50 year: 2021 ident: 10.1016/j.jcss.2023.03.006_br0200 article-title: Parameterized k-clustering: tractability island publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2020.10.005 – year: 2015 ident: 10.1016/j.jcss.2023.03.006_br0130 doi: 10.1007/978-3-319-21275-3 – ident: 10.1016/j.jcss.2023.03.006_br0160 – volume: 34 start-page: 478 issue: 2 year: 2020 ident: 10.1016/j.jcss.2023.03.006_br0190 article-title: Parameterized low-rank binary matrix approximation publication-title: Data Min. Knowl. Discov. doi: 10.1007/s10618-019-00669-5 – volume: vol. 132 start-page: 41:1 year: 2019 ident: 10.1016/j.jcss.2023.03.006_br0120 article-title: On the fixed-parameter tractability of capacitated clustering – volume: 2 start-page: 258 issue: 7 year: 2002 ident: 10.1016/j.jcss.2023.03.006_br0220 article-title: Optimal energy aware clustering in sensor networks publication-title: Sensors doi: 10.3390/s20700258 – start-page: 722 year: 2015 ident: 10.1016/j.jcss.2023.03.006_br0060 article-title: Bi-factor approximation algorithms for hard capacitated k-median problems – volume: 38 start-page: 1382 issue: 4 year: 2008 ident: 10.1016/j.jcss.2023.03.006_br0300 article-title: Closest substring problems with small distances publication-title: SIAM J. Comput. doi: 10.1137/060673898 – volume: 15 start-page: 540 issue: 2 year: 1986 ident: 10.1016/j.jcss.2023.03.006_br0380 article-title: Constant time generation of free trees publication-title: SIAM J. Comput. doi: 10.1137/0215039 – start-page: 952 year: 2005 ident: 10.1016/j.jcss.2023.03.006_br0100 article-title: Approximating k-median with non-uniform capacities – volume: vol. 9682 start-page: 262 year: 2016 ident: 10.1016/j.jcss.2023.03.006_br0070 article-title: An approximation algorithm for uniform capacitated k-median problem with 1+ε capacity violation – volume: 49 start-page: 13 issn: 0178-4617 issue: 1 year: 2007 ident: 10.1016/j.jcss.2023.03.006_br0110 article-title: The complexity of the single individual SNP haplotyping problem publication-title: Algorithmica doi: 10.1007/s00453-007-0029-z – year: 2018 ident: 10.1016/j.jcss.2023.03.006_br0360 article-title: Privacy preserving clustering with constraints – volume: 6 issue: 3 year: 2010 ident: 10.1016/j.jcss.2023.03.006_br0010 article-title: Achieving anonymity via clustering publication-title: ACM Trans. Algorithms doi: 10.1145/1798596.1798602 – start-page: 171 year: 2008 ident: 10.1016/j.jcss.2023.03.006_br0050 article-title: Clustering with balancing constraints – year: 2009 ident: 10.1016/j.jcss.2023.03.006_br0270 doi: 10.1090/chel/367 – year: 1979 ident: 10.1016/j.jcss.2023.03.006_br0210 – volume: 49 start-page: 583 issn: 0003-486X year: 1948 ident: 10.1016/j.jcss.2023.03.006_br0350 article-title: The number of trees publication-title: Ann. Math. (2) doi: 10.2307/1969046 |
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| Snippet | In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task... |
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| StartPage | 171 |
| SubjectTerms | Categorical clustering Fixed-parameterized algorithm k-median Kernelization |
| Title | Parameterized complexity of categorical clustering with size constraints |
| URI | https://dx.doi.org/10.1016/j.jcss.2023.03.006 |
| Volume | 136 |
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