A more relaxed model for graph-based data clustering: S-PLEX CLUSTER EDITING

SIAM Journal on Discrete Mathematics

Volumn 24, Issue 4, 2010, Pages 1662-1683

  Guo, Jiong ^a   Komusiewicz, Christian ^b,c   Niedermeier, Rolf ^b,c   Uhlmann, Johannes ^b,c  

^a SAARLAND UNIVERSITY   (Germany)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Data reduction; Dense subgraphs; Exact algorithms; Fixed parameter tractability; Forbidden subgraph characterization; Graph modification; K plex; NP hard problems

Indexed keywords

EXACT ALGORITHMS; FIXED-PARAMETER TRACTABILITY; FORBIDDEN SUBGRAPH CHARACTERIZATIONS; GRAPH MODIFICATIONS; K-PLEX; NP-HARD PROBLEM; SUBGRAPHS;

CLUSTER ANALYSIS; COMPUTATIONAL COMPLEXITY; PARAMETER ESTIMATION; STATISTICS; TREES (MATHEMATICS);

CLUSTERING ALGORITHMS;

EID: 78751666679     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/090767285     Document Type: Article

References (37)

1. B. BALASUNDARAM, S. BUTENKO, AND I. V. HICKS, Clique relaxations in social network analysis: The maximum k-plex problem, Oper. Res., 2009, to appear.
2. N. BANSAL, A. BLUM, AND S. CHAWLA, Correlation clustering, Mach. Learn., 56(2004), pp. 89-113.
3. R. VAN BEVERN, H. MOSER, AND R. NIEDERMEIER, Kernelization through tidying-a case study based on s-plex cluster vertex deletion, in Proceedings of the 9th LATIN, Lecture Notes in Comput. Sci. 6034, Springer, Berlin, 2010, pp. 528-539.
4. S. BÖCKER, S. BRIESEMEISTER, Q. B. A. BUI, AND A. TRUSS, Going weighted: Parameterized algorithms for cluster editing, Theoret. Comput. Sci., 410(2009), pp. 5467-5480.
5. S. BÖCKER, S. BRIESEMEISTER, AND G. W. KLAU, Exact algorithms for cluster editing: Evaluation and experiments, Algorithmica, 2009, to appear.
6. H. L. BODLAENDER, Kernelization: New upper and lower bound techniques, in Proceedings of the 4th IWPEC, Lecture Notes in Comput. Sci. 5917, Springer, Berlin, 2009, pp. 17-37.
7. J. CHEN AND J. MENG, A 2k kernel for the cluster editing problem, in Proceedings of the 16th COCOON, Lecture Notes in Comput. Sci. 6196, Springer, Berlin, 2010, pp. 459-468.
8. E. J. CHESLER, L. LU, S. SHOU, Y. QU, J. GU, J. WANG, H. C. HSU, J. D. MOUNTZ, N. E. BALDWIN, M. A. LANGSTON, D. W. THREADGILL, K. F. MANLY, AND R. W. WILLIAMS, Complex trait analysis of gene expression uncovers polygenic and pleiotropic networks that modulate nervous system function, Nature Genetics, 37(2005), pp. 233-242.
9. S. COHEN, B. KIMELFELD, AND Y. SAGIV, Generating all maximal induced subgraphs for hereditary and connected-hereditary graph properties, J. Comput. System Sci., 74(2008), pp. 1147-1159.
10. V. J. COOK, S. J. SUN, J. TAPIA, S. Q. MUTH, D. F. ARGÜELLO, B. L. LEWIS, R. B. ROTHENBERG, P. D. MCELROY (the Network Analysis Project Team), Transmission network analysis in tuberculosis contact investigations, J. Infectious Diseases, 196(2007), pp. 1517-1527.
11. F. DEHNE, M. A. LANGSTON, X. LUO, S. PITRE, P. SHAW, AND Y. ZHANG, The cluster editing problem: Implementations and experiments, in Proceedings of the 2nd IWPEC, Lecture Notes in Comput. Sci. 4169, Springer, Berlin, 2006, pp. 13-24.
12. R. G. DOWNEY AND M. R. FELLOWS, Parameterized Complexity, Springer, Berlin, 1999.
13. M. R. FELLOWS, J. GUO, C. KOMUSIEWICZ, R. NIEDERMEIER, AND J. UHLMANN, Graph-based data clustering with overlaps, Discrete Optim., submitted.
14. M. R. FELLOWS, M. A. LANGSTON, F. A. ROSAMOND, AND P. SHAW, Efficient parameterized preprocessing for cluster editing, in Proceedings of the 16th FCT, Lecture Notes in Comput. Sci. 4639, Springer, Berlin, 2007, pp. 312-321.
15. J. FLUM AND M. GROHE, Parameterized Complexity Theory, Springer, Berlin, 2006.
16. J. GRAMM, J. GUO, F. HÜFFNER, AND R. NIEDERMEIER, Graph-modeled data clustering: Exact algorithms for clique generation, Theory Comput. Syst., 38(2005), pp. 373-392.
17. J. GUO, I. A. KANJ, C. KOMUSIEWICZ, AND J. UHLMANN, Editing graphs into disjoint unions of dense clusters, in Proceedings of the 20th ISAAC, Lecture Notes in Comput. Sci. 5878, Springer, Berlin, 2009, pp. 583-593.
18. J. GUO AND R. NIEDERMEIER, Invitation to data reduction and problem kernelization, ACM SIGACT News, 38(2007), pp. 31-45.
19. J. GUO, A more effective linear kernelization for cluster editing, Theoret. Comput. Sci., 410(2009), pp. 718-726.
20. P. HEGGERNES, D. LOKSHTANOV, J. NEDERLOF, C. PAUL, AND J. A. TELLE, Generalized graph clustering: Recognizing (p, q)-cluster graphs, in Proceedings of the 36th WG, Lecture Notes in Comput. Sci. 6410, Springer, Berlin, 2010, pp. 171-183.
21. C. KOMUSIEWICZ, F. HÜFFNER, H. MOSER, AND R. NIEDERMEIER, Isolation concepts for efficiently enumerating dense subgraphs, Theoret. Comput. Sci., 410(2009), pp. 3640-3654.
22. C. KOMUSIEWICZ AND J. UHLMANN, Alternative parameterizations for cluster editing, in Proceedings of the 37th SOFSEM, Lecture Notes in Comput. Sci., to appear.
23. M. KŘIVÁNEK AND J. MORÁVEK, NP-hard problems in hierarchical tree-clustering, Acta Informatica, 23(1986), pp. 311-323.
24. N. MEMON, K. C. KRISTOFFERSEN, D. L. HICKS, AND H. L. LARSEN, Detecting critical regions in covert networks: A case study of 9/11 terrorists network, in Proceedings of the 2nd ARES, IEEE Computer Society, Los Alamitos, CA, 2007, pp. 861-870.
25. H. MOSER, R. NIEDERMEIER, AND M. SORGE, Algorithms and experiments for clique relaxations-finding maximum s-plexes, in Proceedings of the 8th SEA, Lecture Notes in Comput. Sci. 5526, Springer, Berlin, 2009, pp. 233-244.
26. R. NIEDERMEIER AND P. ROSSMANITH, A general method to speed up fixed-parameter-tractable algorithms, Inform. Process. Lett., 73(2000), pp. 125-129.
27. R. NIEDERMEIER, Invitation to Fixed-Parameter Algorithms, Oxford Lecture Ser. Math. Appl. 31, Oxford University Press, Oxford, 2006.
28. F. PROTTI, M. D. DA SILVA, AND J. L. SZWARCFITER, Applying modular decomposition to parameterized cluster editing problems, Theory Comput. Syst., 44(2009), pp. 91-104.
29. S. RAHMANN, T. WITTKOP, J. BAUMBACH, M. MARTIN, A. TRUß, AND S. BÖCKER, Exact and heuristic algorithms for weighted cluster editing, in Proceedings of the 6th CSB, Comput. Syst. Bioinform. 6, Imperial College Press, London, 2007, pp. 391-401.
30. S. E. SCHAEFFER, Graph clustering, Comput. Sci. Rev., 1(2007), pp. 27-64.
31. S. B. SEIDMAN AND B. L. FOSTER, A graph-theoretic generalization of the clique concept, J. Math. Sociology, 6(1978), pp. 139-154.
32. R. SHAMIR, R. SHARAN, AND D. TSUR, Cluster graph modification problems, Discrete Appl. Math., 144(2004), pp. 173-182.
33. R. TARJAN, Depth-first search and linear graph algorithms, SIAM J. Comput., 1(1972), pp. 146-160.
34. T. WITTKOP, J. BAUMBACH, F. P. LOBO, AND S. RAHMANN, Large scale clustering of protein sequences with FORCE-a layout based heuristic for weighted cluster editing, BMC Bioinformatics, 8(2007), p. 396.
35. B. WU AND X. PEI, A parallel algorithm for enumerating all the maximal k-plexes, in Proceedings of the 11th PAKDD, Lecture Notes in Comput. Sci. 4819, Springer, Berlin, 2007, pp. 476-483.
36. R. XU AND D. WUNSCH II, Survey of clustering algorithms, IEEE Trans. Neural Networks, 16(2005), pp. 645-678.
37. A. VAN ZUYLEN AND D. P. WILLIAMSON, Deterministic pivoting algorithms for constrained ranking and clustering problems, Math. Oper. Res., 34(2009), pp. 594-620.