, Volume 71, Issue 2, pp 517–538 | Cite as

Using Patterns to Form Homogeneous Teams

  • Robert Bredereck
  • Thomas Köhler
  • André NichterleinEmail author
  • Rolf Niedermeier
  • Geevarghese Philip


Homogeneous team formation is the task of grouping individuals into teams, each of which consists of members who fulfill the same set of prespecified properties. In this theoretical work, we propose, motivate, and analyze a combinatorial model where, given a matrix over a finite alphabet whose rows correspond to individuals and columns correspond to attributes of individuals, the user specifies lower and upper bounds on team sizes as well as combinations of attributes that have to be homogeneous (that is, identical) for all members of the corresponding teams. Furthermore, the user can define a cost for assigning any individual to a certain team. We show that some special cases of our new model lead to NP-hard problems while others allow for (fixed-parameter) tractability results. For example, the problem is already NP-hard even if (i) there are no lower and upper bounds on the team sizes, (ii) all costs are zero, and (iii) the matrix has only two columns. In contrast, the problem becomes fixed-parameter tractable for the combined parameter “number of possible teams” and “number of different individuals”, the latter being upper-bounded by the number of rows.


Team selection Team formation k-Anonymity Matrix modification problems NP-hardness Parameterized complexity Fixed-parameter tractability Kernelization 



We are grateful to the anonymous referees of the MFCS’11 conference for helping to improve this work by spotting some flaws and providing the idea behind Corollary 4. Furthermore, we thank an anonymous referee for providing the idea of the proof of Theorem 2 which is significantly simpler than the one in the conference version of this paper. We are also grateful to two anonymous Algorithmica reviewers for their constructive feedback.


  1. 1.
    Aamodt, M.G., Kimbrough, W.W.: Effect of group heterogeneity on quality of task solutions. Psychol. Rep. 50(1), 171–174 (1982) CrossRefGoogle Scholar
  2. 2.
    Abdelsalam, H.: Multi-objective team forming optimization for integrated product development projects. In: Foundations of Computational Intelligence, Volume 3. Studies in Computational Intelligence, vol. 203, pp. 461–478. Springer, Berlin (2009) CrossRefGoogle Scholar
  3. 3.
    Adodo, S.O., Agbayewa, J.O.: Effect of homogeneous and heterogeneous ability grouping class teaching on student’s interest, attitude and achievement in integrated science. Int. J. Psychol. Couns. 3(3), 48–54 (2011) Google Scholar
  4. 4.
    Aggarwal, G., Feder, T., Kenthapadi, K., Khuller, S., Panigrahy, R., Thomas, D., Zhu, A.: Achieving anonymity via clustering. ACM Trans. Algorithms 6(3), 1–19 (2010) CrossRefMathSciNetGoogle Scholar
  5. 5.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, New York (1993) zbMATHGoogle Scholar
  6. 6.
    Baykasoglu, A., Dereli, T., Das, S.: Project team selection using fuzzy optimization approach. Cybern. Syst. 38(2), 155–185 (2007) CrossRefzbMATHGoogle Scholar
  7. 7.
    Blocki, J., Williams, R.: Resolving the complexity of some data privacy problems. In: Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP’10). LNCS, vol. 6199, pp. 393–404. Springer, Berlin (2010) CrossRefGoogle Scholar
  8. 8.
    Kernelization, H.L.B.: New upper and lower bound techniques. In: Proceedings of the 4th International Workshop on Parameterized and Exact Computation (IWPEC’09). LNCS, vol. 5917, pp. 17–37. Springer, Berlin (2009) CrossRefGoogle Scholar
  9. 9.
    Bodlaender, H.L., Thomassé, S., Yeo, A.: Kernel bounds for disjoint cycles and disjoint paths. Theor. Comput. Sci. 412(35), 4570–4578 (2011) CrossRefzbMATHGoogle Scholar
  10. 10.
    Bredereck, R., Nichterlein, A., Niedermeier, R., Philip, G.: The effect of homogeneity on the computational complexity of combinatorial data anonymization. Data Min. Knowl. Discov. (2012). Online available Google Scholar
  11. 11.
    Bredereck, R., Nichterlein, A., Niedermeier, R.: Pattern-guided k-anonymity. In: Proceedings of the Joint Conference of the 7th International Frontiers of Algorithmics Workshop and the 9th International Conference on Algorithmic Aspects of Information and Management (FAW-AAIM’13). LNCS, vol. 7924, pp. 350–361. Springer, Berlin (2013) CrossRefGoogle Scholar
  12. 12.
    Cygan, M., Pilipczuk, M., Pilipczuk, M., Wojtaszczyk, J.: Solving the 2-disjoint connected subgraphs problem faster than 2n. In: Proceedings of the 10th Latin American Symposium on Theoretical Informatics (LATIN’12). LNCS, vol. 7256, pp. 195–206. Springer, Berlin (2012) CrossRefGoogle Scholar
  13. 13.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Berlin (1999) CrossRefGoogle Scholar
  14. 14.
    Fellows, M.R., Jansen, B.M., Rosamond, F.: Towards fully multivariate algorithmics: parameter ecology and the deconstruction of computational complexity. Eur. J. Comb. 34, 541–566 (2013) CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006) Google Scholar
  16. 16.
    Fung, B.C.M., Wang, K., Chen, R., Yu, P.S.: Privacy-preserving data publishing: a survey of recent developments. ACM Comput. Surv. 42(4), 14:1–14:53 (2010) CrossRefGoogle Scholar
  17. 17.
    Guo, J., Niedermeier, R.: Invitation to data reduction and problem Kernelization. SIGACT News 38(1), 31–45 (2007) CrossRefGoogle Scholar
  18. 18.
    Köhler, T.: Benutzergeführtes Anonymisieren von Daten mit Pattern Clustering: Algorithmen und Komplexität (in German, English title: User-guided data anonymization with pattern clustering: Algorithms and complexity). Diploma thesis, Friedrich-Schiller-Universität Jena (2011). Available at
  19. 19.
    Kuo, S., Fuchs, W.: Efficient spare allocation for reconfigurable arrays. IEEE Des. Test Comput. 4(1), 24–31 (1987) CrossRefGoogle Scholar
  20. 20.
    Lappas, T., Liu, K., Terzi, E.: Finding a team of experts in social networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’09), pp. 467–476. ACM, New York (2009) CrossRefGoogle Scholar
  21. 21.
    Lokshtanov, D., Misra, N., Saurabh, S.: Kernelization—preprocessing with a guarantee. In: The Multivariate Algorithmic Revolution and Beyond. LNCS, vol. 7370, pp. 129–161. Springer, Berlin (2012) CrossRefGoogle Scholar
  22. 22.
    Majumder, A., Datta, S., Naidu, K.: Capacitated team formation problem on social networks. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’12), pp. 1005–1013. ACM, New York (2012) CrossRefGoogle Scholar
  23. 23.
    Meyerson, A., Williams, R.: On the complexity of optimal k-anonymity. In: Proceedings of the 23rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS’04), pp. 223–228. ACM, New York (2004) Google Scholar
  24. 24.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006) CrossRefzbMATHGoogle Scholar
  25. 25.
    Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS’10). Leibniz International Proceedings in Informatics (LIPIcs), vol. 5, pp. 17–32. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Wadern (2010) Google Scholar
  26. 26.
    Orlin, J.: A faster strongly polynomial minimum cost flow algorithm. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC’88), pp. 377–387. ACM, New York (1988) Google Scholar
  27. 27.
    Samarati, P.: Protecting respondents identities in microdata release. IEEE Trans. Knowl. Data Eng. 13(6), 1010–1027 (2001) CrossRefGoogle Scholar
  28. 28.
    Samarati, P., Sweeney, L.: Generalizing data to provide anonymity when disclosing information. In: Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS’98), p. 188. ACM, New York (1998) Google Scholar
  29. 29.
    Sweeney, L.: Uniqueness of simple demographics in the U.S. population. Technical report, Carnegie Mellon University, School of Computer Science, Laboratory for International Data Privacy (2000) Google Scholar
  30. 30.
    Sweeney, L.: k-Anonymity: a model for protecting privacy. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10(5), 557–570 (2002) CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    White, K.B.: A preliminary investigation of information systems team structures. Inf. Manag. 7(6), 331–335 (1984) CrossRefGoogle Scholar
  32. 32.
    Wi, H., Oh, S., Mun, J., Jung, M.: A team formation model based on knowledge and collaboration. Expert Syst. Appl. 36(5), 9121–9134 (2009) CrossRefGoogle Scholar
  33. 33.
    Zzkarian, A., Kusiak, A.: Forming teams: an analytical approach. IIE Trans. 31(1), 85–97 (1999) Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Thomas Köhler
    • 3
  • André Nichterlein
    • 1
    Email author
  • Rolf Niedermeier
    • 1
  • Geevarghese Philip
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Friedrich-Schiller-Universität JenaJenaGermany

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