Algorithmica

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

Using Patterns to Form Homogeneous Teams

  • Robert Bredereck
  • Thomas Köhler
  • André Nichterlein
  • Rolf Niedermeier
  • Geevarghese Philip
Article

Abstract

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.

Keywords

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

Notes

Acknowledgements

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.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Robert Bredereck
    • 1
  • Thomas Köhler
    • 3
  • André Nichterlein
    • 1
  • 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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