Skip to main content
Springer Nature Link
Log in

Cluster Editing

  • Conference paper
The Nature of Computation. Logic, Algorithms, Applications (CiE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7921))

Included in the following conference series:

Abstract

The Cluster Editing problem asks to transform a graph into a disjoint union of cliques using a minimum number of edge modifications. Although the problem has been proven NP-complete several times, it has nevertheless attracted much research both from the theoretical and the applied side. The problem has been the inspiration for numerous algorithms in bioinformatics, aiming at clustering entities such as genes, proteins, phenotypes, or patients. In this paper, we review exact and heuristic methods that have been proposed for the Cluster Editing problem, and also applications of these algorithms for biological problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
€34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 53.49
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

') var buybox = document.querySelector("[data-id=id_"+ timestamp +"]").parentNode var buyingOptions = buybox.querySelectorAll(".buying-option") ;[].slice.call(buyingOptions).forEach(initCollapsibles) var buyboxMaxSingleColumnWidth = 480 function initCollapsibles(subscription, index) { var toggle = subscription.querySelector(".buying-option-price") subscription.classList.remove("expanded") var form = subscription.querySelector(".buying-option-form") var priceInfo = subscription.querySelector(".price-info") var buyingOption = toggle.parentElement if (toggle && form && priceInfo) { toggle.setAttribute("role", "button") toggle.setAttribute("tabindex", "0") toggle.addEventListener("click", function (event) { var expandedBuyingOptions = buybox.querySelectorAll(".buying-option.expanded") var buyboxWidth = buybox.offsetWidth ;[].slice.call(expandedBuyingOptions).forEach(function(option) { if (buyboxWidth buyboxMaxSingleColumnWidth) { toggle.click() } else { if (index === 0) { toggle.click() } else { toggle.setAttribute("aria-expanded", "false") form.hidden = "hidden" priceInfo.hidden = "hidden" } } }) } initialStateOpen() if (window.buyboxInitialised) return window.buyboxInitialised = true initKeyControls() })()

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Sharan, R., Maron-Katz, A., Shamir, R.: CLICK and EXPANDER: a system for clustering and visualizing gene expression data. Bioinformatics 19(14), 1787–1799 (2003)

    Article  Google Scholar 

  2. Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. J. Comput. Biol. 6(3-4), 281–297 (1999)

    Article  Google Scholar 

  3. Hartuv, E., Schmitt, A.O., Lange, J., Meier-Ewert, S., Lehrach, H., Shamir, R.: An algorithm for clustering cDNA fingerprints. Genomics 66(3), 249–256 (2000)

    Article  Google Scholar 

  4. Zahn Jr., C.T.: Approximating symmetric relations by equivalence relations. J. Soc. Indust. Appl. Math. 12(4), 840–847 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  5. Moon, J.W.: A note on approximating symmetric relations by equivalence classes. Siam J. Appl. Math. 14(2), 226–227 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  6. Rahmann, S., Wittkop, T., Baumbach, J., Martin, M., Truss, A., Böcker, S.: Exact and heuristic algorithms for weighted cluster editing. In: Proc. of Computational Systems Bioinformatics (CSB 2007), vol. 6, pp. 391–401 (2007)

    Google Scholar 

  7. Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45, 52–96 (1989)

    Article  Google Scholar 

  8. Kochenberger, G.A., Glover, F., Alidaee, B., Wang, H.: Clustering of microarray data via clique partitioning. J. Comb. Optim. 10(1), 77–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Delvaux, S., Horsten, L.: On best transitive approximations to simple graphs. Acta. Inform. 40(9), 637–655 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144(1-2), 173–182 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1), 89–113 (2004)

    Article  MATH  Google Scholar 

  12. Křivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta Inform. 23(3), 311–323 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Komusiewicz, C., Uhlmann, J.: Cluster editing with locally bounded modifications. Discrete Appl. Math. 160(15), 2259–2270 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mannaa, B.: Cluster editing problem for points on the real line: A polynomial time algorithm. Inform. Process. Lett. 110, 961–965 (2010)

    Article  MathSciNet  Google Scholar 

  16. Böcker, S.: A golden ratio parameterized algorithm for cluster editing. J. Discrete Algorithms 16, 79–89 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Berlin (1999)

    Book  Google Scholar 

  18. Cao, Y., Chen, J.: Cluster editing: Kernelization based on edge cuts. Algorithmica 64(1), 152–169 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Fomin, F.V., Kratsch, S., Pilipczuk, M., Pilipczuk, M., Villanger, Y.: Tight bounds for parameterized complexity of cluster editing. In: Proc. of Symposium on Theoretical Aspects of Computer Science (STACS 2013). LIPIcs, vol. 20, pp. 32–43. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2013)

    Google Scholar 

  20. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. System Sci. 71(3), 360–383 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: Ranking and clustering. J. ACM 55(5), Article 23 (2008)

    Google Scholar 

  22. van Zuylen, A., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. Math. Oper. Res. 34(3), 594–620 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Vescia, G.: Descriptive classification of cetacea: whales, porpoises and dolphins. In: Marcotorchino, J., Proth, J.M., Janssen, J. (eds.) Data Analysis in Real Life Environment: Ins and Outs of Solving Problems, pp. 7–14. Elsevier Science, North-Holland, Amsterdam (1985)

    Google Scholar 

  24. Vescia, G.: Automatic classification of cetaceans by similarity aggregation. In: Marcotorchino, J., Proth, J.M., Janssen, J. (eds.) Data Analysis in Real Life Environment: Ins and Outs of Solving Problems, pp. 15–24. Elsevier Science, North-Holland, Amsterdam (1985)

    Google Scholar 

  25. Marcotorchino, J., Michaud, P.: Heuristic approach to the similarity aggregation problem. Methods of Operations Research 43, 395–404 (1981)

    MATH  Google Scholar 

  26. Marcotorchino, J., Michaud, P.: Optimization in exploratory data analysis. In: Proc. of Symposium on Operations Research, Köln, Germany. Physica Verlag (1981)

    Google Scholar 

  27. Schader, M., Tüshaus, U.: Ein Subgradientenverfahren zur Klassifikation qualitativer Daten. Operations Research Spektrum 7, 1–5 (1985)

    Article  MATH  Google Scholar 

  28. Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. Algorithmica 60(2), 316–334 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 289–302. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  30. Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixed-parameter algorithms for clique generation. Theory Comput. Syst. 38(4), 373–392 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: Parameterized algorithms for cluster editing. Theor. Comput. Sci. 410(52), 5467–5480 (2009)

    Article  MATH  Google Scholar 

  33. Böcker, S., Damaschke, P.: Even faster parameterized cluster deletion and cluster editing. Inform. Process. Lett. 111(14), 717–721 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  34. Protti, F., da Silva, M.D., Szwarcfiter, J.L.: Applying modular decomposition to parameterized cluster editing problems. Theory Comput. Syst. 44(1), 91–104 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Fellows, M.R.: The lost continent of polynomial time: Preprocessing and kernelization. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 276–277. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  36. Fellows, M.R., Langston, M.A., Rosamond, F.A., Shaw, P.: Efficient parameterized preprocessing for cluster editing. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 312–321. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  37. Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410(8-10), 718–726 (2009)

    Article  MATH  Google Scholar 

  38. Chen, J., Meng, J.: A 2k kernel for the cluster editing problem. J. Comput. Syst. Sci. 78(1), 211–220 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Golub, T.R., Slonim, D.K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J.P., Coller, H., Loh, M.L., Downing, J.R., Caligiuri, M.A., Bloomfield, C.D., Lander, E.S.: Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring. Science 286(5439), 531–537 (1999)

    Article  Google Scholar 

  40. Wittkop, T., Baumbach, J., Lobo, F.P., Rahmann, S.: Large scale clustering of protein sequences with FORCE — a layout based heuristic for weighted cluster editing. BMC Bioinformatics 8, 396 (2007)

    Article  Google Scholar 

  41. Wittkop, T., Emig, D., Lange, S., Rahmann, S., Albrecht, M., Morris, J.H., Böcker, S., Stoye, J., Baumbach, J.: Partitioning biological data with transitivity clustering. Nat. Methods 7(6), 419–420 (2010)

    Article  Google Scholar 

  42. Smoot, M.E., Ono, K., Ruscheinski, J., Wang, P.L., Ideker, T.: Cytoscape 2.8: new features for data integration and network visualization. Bioinformatics 27(3), 431–432 (2011)

    Article  Google Scholar 

  43. Morris, J.H., Apeltsin, L., Newman, A.M., Baumbach, J., Wittkop, T., Su, G., Bader, G.D., Ferrin, T.E.: clusterMaker: a multi-algorithm clustering plugin for Cytoscape. BMC Bioinformatics 12, 436 (2011)

    Article  Google Scholar 

  44. Cerdeira, L.T., Carneiro, A.R., Ramos, R.T.J., de Almeida, S.S., D’Afonseca, V., Schneider, M.P.C., Baumbach, J., Tauch, A., McCulloch, J.A., Azevedo, V.A.C., Silva, A.: Rapid hybrid de novo assembly of a microbial genome using only short reads: Corynebacterium pseudotuberculosis I19 as a case study. J. Microbiol. Methods 86(2), 218–223 (2011)

    Article  Google Scholar 

  45. Baumbach, J., Tauch, A., Rahmann, S.: Towards the integrated analysis, visualization and reconstruction of microbial gene regulatory networks. Brief Bioinform. 10(1), 75–83 (2009)

    Article  Google Scholar 

  46. Baumbach, J.: On the power and limits of evolutionary conservation–unraveling bacterial gene regulatory networks. Nucleic Acids Res. 38(22), 7877–7884 (2010)

    Article  Google Scholar 

  47. Röttger, R., Kalaghatgi, P., Sun, P., Soares, S.C., Azevedo, V., Wittkop, T., Baumbach, J.: Density parameter estimation for finding clusters of homologous proteins–tracing actinobacterial pathogenicity lifestyles. Bioinformatics 29(2), 215–222 (2013)

    Article  Google Scholar 

  48. Röttger, R., Kreutzer, C., Vu, T.D., Wittkop, T., Baumbach, J.: Online transitivity clustering of biological data with missing values. In: Proc. of German Conference on Bioinformatics (GCB 2012), pp. 57–68 (2012)

    Google Scholar 

  49. Sakai, S., Takaki, Y., Shimamura, S., Sekine, M., Tajima, T., Kosugi, H., Ichikawa, N., Tasumi, E., Hiraki, A.T., Shimizu, A., Kato, Y., Nishiko, R., Mori, K., Fujita, N., Imachi, H., Takai, K.: Genome sequence of a mesophilic hydrogenotrophic methanogen methanocella paludicola, the first cultivated representative of the order methanocellales. PLoS One 6(7), e22898 (2011)

    Google Scholar 

  50. Jochmann, N., Kurze, A.K., Czaja, L.F., Brinkrolf, K., Brune, I., Hüser, A.T., Hansmeier, N., Pühler, A., Borovok, I., Tauch, A.: Genetic makeup of the Corynebacterium glutamicum LexA regulon deduced from comparative transcriptomics and in vitro DNA band shift assays. Microbiology 155(pt. 5), 1459–1477 (2009)

    Article  Google Scholar 

  51. Baumbach, J., Rahmann, S., Tauch, A.: Reliable transfer of transcriptional gene regulatory networks between taxonomically related organisms. BMC Syst. Biol. 3, 8 (2009)

    Article  Google Scholar 

  52. Pauling, J., Röttger, R., Tauch, A., Azevedo, V., Baumbach, J.: CoryneRegNet 6.0—updated database content, new analysis methods and novel features focusing on community demands. Nucleic Acids Res. 40(Database issue), D610–D614 (2012)

    Article  Google Scholar 

  53. Pauling, J., Röttger, R., Neuner, A., Salgado, H., Collado-Vides, J., Kalaghatgi, P., Azevedo, V., Tauch, A., Pühler, A., Baumbach, J.: On the trail of EHEC/EAEC—unraveling the gene regulatory networks of human pathogenic Escherichia coli bacteria. Integr. Biol. (Camb.) 4(7), 728–733 (2012)

    Article  Google Scholar 

  54. Wittkop, T., Emig, D., Truss, A., Albrecht, M., Böcker, S., Baumbach, J.: Comprehensive cluster analysis with transitivity clustering. Nat. Protocols 6, 285–295 (2011)

    Article  Google Scholar 

  55. Hauschild, A.C., Schneider, T., Pauling, J., Rupp, K., Jang, M., Baumbach, J., Baumbach, J.: Computational methods for metabolomics data analysis of ion mobility spectrometry data — reviewing the state of the art. Metabolites 2(4), 733–755 (2012)

    Article  Google Scholar 

  56. Wittkop, T., Rahmann, S., Böcker, S., Baumbach, J.: Extension and robustness of transitivity clustering for protein-protein interaction network analysis. Internet Math. 7(4), 255–273 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  57. Robertson, A.L., Bate, M.A., Buckle, A.M., Bottomley, S.P.: The rate of polyQ-mediated aggregation is dramatically affected by the number and location of surrounding domains. J. Mol. Biol. 413(4), 879–887 (2011)

    Article  Google Scholar 

  58. Pacheco, L.G.C., Slade, S.E., Seyffert, N., Santos, A.R., Castro, T.L.P., Silva, W.M., Santos, A.V., Santos, S.G., Farias, L.M., Carvalho, M.A.R., Pimenta, A.M.C., Meyer, R., Silva, A., Scrivens, J.H., Oliveira, S.C., Miyoshi, A., Dowson, C.G., Azevedo, V.: A combined approach for comparative exoproteome analysis of Corynebacterium pseudotuberculosis. BMC Microbiol. 11(1), 12 (2011)

    Article  Google Scholar 

  59. Wittkop, T., Berman, A.E., Fleisch, K.M., Mooney, S.D.: DEFOG: discrete enrichment of functionally organized genes. Integr. Biol (Camb) 4(7), 795–804 (2012)

    Article  Google Scholar 

  60. Marx, D., Razgon, I.: Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: Proc. of ACM Symposium on Theory of Computing (STOC 2011), pp. 469–478. ACM press, New York (2011)

    Google Scholar 

  61. Bousquet, N., Daligault, J., Thomassé, S.: Multicut is FPT. In: Proc. of ACM Symposium on Theory of Computing (STOC 2011), pp. 459–468. ACM press, New York (2011)

    Google Scholar 

  62. Damaschke, P.: Fixed-parameter enumerability of cluster editing and related problems. Theory Comput. Syst. 46(2), 261–283 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  63. Komusiewicz, C., Uhlmann, J.: Alternative parameterizations for cluster editing. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 344–355. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  64. Damaschke, P.: Bounded-degree techniques accelerate some parameterized graph algorithms. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 98–109. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  65. Weller, M., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: On making directed graphs transitive. J. Comput. Syst. Sci. 78(2), 559–574 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  66. Böcker, S., Briesemeister, S., Klau, G.W.: On optimal comparability editing with applications to molecular diagnostics. BMC Bioinformatics 10(suppl. 1), S61 (2009); Proc. of Asia-Pacific Bioinformatics Conference (APBC 2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair for Bioinformatics, Friedrich-Schiller-University, Jena, Germany

    Sebastian Böcker

  2. Computational Biology Research Group, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Jan Baumbach

Authors
  1. Sebastian Böcker
    View author publications

    Search author on:PubMed Google Scholar

  2. Jan Baumbach
    View author publications

    Search author on:PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento die Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126, Milan, Italy

    Paola Bonizzoni

  2. Institute for Theoretical Computer Science, Mathematics and Operations Research, Faculty of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Vasco Brattka

  3. Institute for Logic, Language and Computation, University of Amsterdam, Postbus 94242, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Böcker, S., Baumbach, J. (2013). Cluster Editing. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39053-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39052-4

  • Online ISBN: 978-3-642-39053-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics