On the hardness of labeled correlation clustering problem: A parameterized complexity view

Motivated by practical applications, the Labeled Correlation Clustering problem, a variant of Correlation Clustering problem, is formally defined and studied in this paper. Since the problem is NP-complete, we consider the parameterized complexities. Three different parameterizations are considered, and the corresponding parameterized complexities are studied. For the two parameterized problems which are fixed-parameter-tractable, the lower bounds of them are analyzed under SETH (Strong Exponential Time Hypothesis).

[1]  Somesh Jha,et al.  Two formal analyses of attack graphs , 2002, Proceedings 15th IEEE Computer Security Foundations Workshop. CSFW-15.

[2]  Rajeev Motwani,et al.  Robust identification of fuzzy duplicates , 2005, 21st International Conference on Data Engineering (ICDE'05).

[3]  Russell Impagliazzo,et al.  Which Problems Have Strongly Exponential Complexity? , 2001, J. Comput. Syst. Sci..

[4]  Michael R. Fellows,et al.  FIXED-PARAMETER TRACTABILITY AND COMPLETENESS , 2022 .

[5]  Refael Hassin,et al.  Approximation algorithms and hardness results for labeled connectivity problems , 2006, J. Comb. Optim..

[6]  Venkatesan Guruswami,et al.  Clustering with qualitative information , 2005, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[7]  Jianzhong Li,et al.  Algorithms and complexity results for labeled correlation clustering problem , 2015, J. Comb. Optim..

[8]  Amos Fiat,et al.  Correlation clustering in general weighted graphs , 2006, Theor. Comput. Sci..

[9]  Jin-Yi Cai,et al.  Approximation and hardness results for label cut and related problems , 2009, J. Comb. Optim..

[10]  Michael R. Fellows,et al.  Fixed-parameter tractability and completeness III: some structural aspects of the W hierarchy , 1993 .

[11]  Dmitri V. Kalashnikov,et al.  Exploiting context analysis for combining multiple entity resolution systems , 2009, SIGMOD Conference.

[12]  Moni Naor,et al.  Rank aggregation methods for the Web , 2001, WWW '01.

[13]  Gerhard J. Woeginger,et al.  Paths and cycles in colored graphs , 2001, Australas. J Comb..

[14]  Hwee Tou Ng,et al.  A Machine Learning Approach to Coreference Resolution of Noun Phrases , 2001, CL.

[15]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[16]  Gerhard J. Woeginger,et al.  Local search for the minimum label spanning tree problem with bounded color classes , 2003, Oper. Res. Lett..

[17]  D. Berend,et al.  IMPROVED BOUNDS ON BELL NUMBERS AND ON MOMENTS OF SUMS OF RANDOM VARIABLES , 2000 .

[18]  Ahmed K. Elmagarmid,et al.  Duplicate Record Detection: A Survey , 2007, IEEE Transactions on Knowledge and Data Engineering.

[19]  Avrim Blum,et al.  Correlation Clustering , 2004, Machine Learning.

[20]  Martin Grohe,et al.  Parameterized complexity for the database theorist , 2002, SGMD.

[21]  Michael R. Fellows,et al.  The parameterized complexity of some minimum label problems , 2009, J. Comput. Syst. Sci..

[22]  Jörg Flum,et al.  Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[23]  Robert D. Carr,et al.  On the red-blue set cover problem , 2000, SODA '00.

[24]  Russell Impagliazzo,et al.  On the Complexity of k-SAT , 2001, J. Comput. Syst. Sci..

[25]  Yoshio Okamoto,et al.  On Problems as Hard as CNF-SAT , 2011, 2012 IEEE 27th Conference on Computational Complexity.

[26]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[27]  Michael R. Fellows,et al.  Fixed-Parameter Tractability and Completeness II: On Completeness for W[1] , 1995, Theor. Comput. Sci..